Everything the show did well:
-Decent hero cast overall. Everyone in the hero team feels useful to a degree and can fight untransformed, which helps them stay relevant throughout the show.
-Consistently entertaining villains from start to finish.
-Pretty entertaining monsters and characters of the week for most of the show.
-Pretty great action outside of the constant use of CGI; Gotchard Igniter and Kamen Rider Valvarad in particular come to mind.
-Some interesting concepts in the world-building and story here and there.
-Pretty great soundtrack.

Everything the show did bad:
-This is the Kamen Rider season that has the most spin-offs that are essential to the plot, which makes the story feel incomplete and disjointed. Usually one doesn't need to watch specials and movies to understand a show; at most they introduce a movie character for 1 episode and not properly explain the character to make the viewer want to watch the movie, but they usually aren't that essential. Even when specials are essential for a season, there usually aren't many, and one can watch them after the show is over and still get about the same experience.
However, Gotchard has too many cases where these spin-offs matter. One of the recurring villains of the first quarter suddenly stops appearing; this is because his arc gets resolved in the winter crossover movie with Geats. Said movie introduces the powers of Rinne, who's supposed to be the second most important character in the show, and the show doesn't do a proper job at summarizing the movie in order to understand where her powers come from. The second quarter has the protagonist Houtaro getting a mentor, which leads to him getting an upgrade; however said mentor's character arc gets resolved in this show's summer movie and he barely appears for the rest of the show's run past the second quarter. The third quarter has a whole mini-arc dedicated to Kaguya Quartz a character from the Kamen Rider Legend spin-off, said special and mini-arc have several references to past rider shows and the crossover mini-series Kamen Rider Outsiders.
-Despite Toei's kodomo Tokusatsu not really being known for having good acting, the acting of this show's main duo Houtaro and Rinne is way worse than usual. Houtaro's actor Junsei Motojima at least improves enough after the first quarter outside his occasional weird stare, so he's not really that big of an issue. But Rinne's actress Reiyo Matsumoto while she definitely improves, never improves enough to be considered a good actress, so despite her character having the most consistently well-written character out of the main trio, the fact that she gets her main powers in a movie and the actress consistently having poor delivery for the character's emotional scenes, end up making it hard to care for the character.
-The show fails at giving Houtaro a proper motivation besides empathy to care for the chemies which makes his whole character feel cheap most of the time despite him developing a proper friendship with Hopper1 and most chemies of the week. While episode 18 does give a better explanation of why he wants to befriend all chemies it also opens a bunch of other questions that aren't answered in the show, so it doesn't really fix this issue.
-The show fails at making proper use of its setting. They hardly ever do any proper alchemy and instead it just evolves into being used as normal magic or transmutation. The alchemy academy barely feels like an academy and hardly ever shows them practicing to become better alchemists after the first quarter, this really affects Houtaro's character since he's the newest of the team and is almost never shown doing alchemy or trying to get better at it until Rainbow Gotchard, he should have made the connection with cooking way earlier in the show so that his progression feels more natural, because of this, the final episode feels way less engaging. The school setting feels very disconnected from the main plot, which makes a character like Kajiki, while likeable overall, not really accomplish anything and not hang out with the cast that much during the show's middle. The alchemy sages pretty much don't matter for the show, which makes the alchemist organization barely have any background or any interesting traits, most of the important world-building elements and lore end up coming from the villain Giggist.
-Spanner's arc in the first quarter feels unnecessary and makes so that the character doesn't have proper set up or foreshadowing for his later arcs even if they're competently written.
-After the first quarter, Sabimaru and Renge don't get much to do. Sabimaru at least gets a 2 parter near the end to close his character arc and show how much he's grown, but Renge basically gets nothing, even her backstory episode barely focuses on her.
-Despite Minato's backstory being great, his actions in the show's middle are not justified enough. After Houtaro obtains CrossHopper, he doesn't get much to do despite the show setting him to change the alchemist's order.
-Fuga is a severely underutilized character, which makes it hard to care for him despite his cool moments.
-Clotho loses too many battles to be taken seriously. Out of the 3 sisters she's the one who gets treated the worst.
-Despite Lachesis getting a lot of cool developments throughout the show, it also feels like she barely gets to do something in the second half. She also barely fights despite getting new powers in episode 33.
-Germain and Gaelijah are kind of forgettable.
-Despite Geryon's actions making sense due to the kind of character he is and being a very entertaining villain overall, his main goal is still kind of hard to take seriously. It feels that his backstory should have been explored further since we only get a brief dialogue from Giggist explaining his origins.
-Kaguya and his personal villains are extremely disconnected from the show, which makes his mini-arc feel out place even if it does progress the story.
-While the content of the final arc is good for the most part, it still feels really rushed. The villains in the final arc get the short end of the stick, it feels that Rinne and Spanner didn't get the most use of their new powers and due to the Ouroboros Realm existing it doesn't feel like the finale has much emotional weight.
-Some pretty bad/forgettable monsters/cases of the week in the first quarter of the show.
-Due to the chemmies barely having any character besides Hopper1, not being able to talk besides Nijigon and mostly having to stay in their card form throughout most of the show, they end up being just kind of OK mascots, with the exception of Hopper1 which is pretty good despite not being anything stand-out.

Reasons for the show's strengths:
Main writer Keiichi Hasegawa is really great at writing villains. The other main writer Hiroki Uchida did a pretty good job at following the plot-points Hasegawa set up. Secondary writer Akiko Inoue was good at giving Rinne more characterization and also managed to add some good comedic elements.

Reasons for the show's problems:
Chief producer Yousuke Minato, prior to Gotchard was chosen by Omori to be a co-producer for King-Ohger alongside Mochizuki. Omori wanted to stop working for Kamen Rider since he felt he was out of ideas and thus wanted to produce a Super Sentai show, in order to increase the chances for the show to be greenlit, he wanted to work on the pre-production earlier in secret as a trio of producers, Minato would end up developing the countries of Ishabana and Toufu. Ultimately, the show ended up being greenlit under the condition that Omori would work on the show alone from that point onward. The reason for their removal was that Mochizuki had just been demoted due to his work in Revice and that they wanted Minato to produce the next Kamen Rider show.
Toei wanted to make a more lighthearted season of Kamen Rider since the previous season Geats was darker than usual. Then, when King-Ohger ended up being more popular with adults than children, Toei really wanted to emphasize the lighthearted elements even more in order to "bring tokusatsu back to the children", the next Sentai Boonboomger would also fall under this philosophy. Due to this, Toei wanted Minato to be the next producer in order to train the next generation of producers and because he prefers lighthearted shows.
Due to him being a new producer and the fear that this show would also fall into the pitfalls that Revice did, which was made by a relatively new producer, promoted producers Shin-ichiro Shirakura and Hideaki Tsukuda helped with the show pre-production. Shirakura came up with the idea of having cards as a gimmick, that said cards wouldn't be used for an OCG/TCG and for the show to have a school setting. Minato then came up for the cards to feature monsters inspired by Pokémon and Digimon and that there should be 100 or more cards to collect, since they couldn't use that many cards for individual forms. Tsukuda came up with the idea of using 2 cards for each and forms and decided that the show should have an emphasis on alchemy so that the fusion of cards makes sense.
Usually for most Toei tokusatsu the producer comes up with the setting and checks up throughout the show so that the setting is realized properly by the writer, but in this case he barely came up with any of the ideas of the setting, so it's speculated that this is the main reason why alchemy and the school setting are so half-baked in the show. The only idea that we know he came up with was the creation of Rinne and that she should be the secondary rider, so that's probably why writing wise she's the most consistent one in the cast.
Minato would end up choosing Hiroki Uchida as the main writer due to him having worked with him with Kamen Rider Outsiders. Uchida suffers from the same issue as Nobuhiro Mouri, they're good at following ideas from another writer under proper supervision, which is why they most often work as episode writers. However, they don't work well because they're bad at coming up with their own ideas, so when they do they come up with pretty generic stuff. The original plan for Gotchard by Uchida was for Houtaro to be a student with no direction in his life and ultimately finds the chemies imprisoned, due to their state of being trapped in cards he would free them since he sympathized with them due to both being pathetic, this would ultimately create chaos as the chemies become evil in the presence of people with ill-intentions, due to this event being his fault, Houtaro takes responsibility and decides to catch all the chemies while befriending them. It was planned for there to be no main villains besides the demon from the book, instead the show would have consisted on the cast solving cases of the week up to the final arc with barely any plot progression. Ultimately, Toei higher ups thought that this premise was too bland and decided that Keiichi Hasegawa, who had already been chosen to be an episode writer, should be this show's co-writer alongside Uchida. The reason they chose him was because Minato has mostly been an assistant producer for anime up to this point, so since Hasegawa was a writer who had lots of experience with both anime and tokusatsu, they felt that he would be a good fit for the show.
However this decision was made somewhat late into pre-production, so there was some stuff they weren't able to change. Ultimately, Hasegawa would create this show's villains, who ended up being the best aspect of the show and changed how the chemies got released in order for them to make sense with the new villains. However this change made Houtaro's sympathy for the chemies make way less sense which really affected his character for the worse.
Hasegawa prefers writing darker stories but since Minato wanted this show to be more lighthearted, he would suppress most of Hasegawa's ideas in the first quarter and they would have many creative clashes. Ultimately after his ideas and villains ended up being the most well-received aspects of the show, he would end up writing most of the show's story, world-building, and Spanner's character after the first quarter, while Uchida built up on his ideas and focused on writing Houtaro's character (which is probably why Houtaro was the most sloppily written, he also was the one who decided the show's ending). They didn't know on what direction to take Rinne so the producer got Akiko Inoue to be a secondary writer to give Rinne more characterization. After this, from the second quarter onward, the show improves since now it has a proper direction, but the setup is very flawed due to how directionless the first quarter was.
Due to Kamen Rider's main demographic being really young boys and adult otakus, they didn't believe that Majade would sell well, so they wanted her toys to be premium bandai. However the producer thought that in order for her toys to sell better and for her to be more popular she should get her powers in the movie instead of the show, which negatively affected her character.
In order to maximize sales, Minato wanted the movies to relate to the plot, which is why characters like Licht Kugimiya and Daybreak ended up that way.
Prior to the show release, since Majade was going to be premium bandai, Minato had decided that the retail toys that usually go to the secondary should go to Kamen Rider Legend, a mini-series that focused on crossover aspects, and then introduce said Rider into the show proper in order to bring older fans of the franchise into the show. Since these decisions had already been decided prior to Hasegawa taking over for most of the plot, the mini-arc of Legend ended up happening anyway.
The staff had decided that Majade's and Valvarad's final power-ups should happen at the very end so that they feel like they're "the strongest" forms, since they happen too late to lose to a villain. The final power-up Gotchard gets in the final episode was decided at the last minute by Bandai since the transformation item had already opened for pre-orders due to the summer movie.
Some people speculate that the reason for Houtaro's and Rinne's actors being worse than usual is due to Minato having worked mostly on anime, so when doing casting he chose more arbitrarily. Usually casting is done with the main writer and the pilot director, but people speculate due to the phrasing in some interviews that they were both cast when Uchida was the sole writer for the show and he just didn't mind it due to him mostly being an episode writer. Then the villains, and most main characters introduced later had way better actors since they were cast after Hasegawa had joined the project. But these are purely theories since we don't know how early the main duo were cast.
Some leaks indicate that Shirakura was more involved in the show than it initially seemed, but it's unknown what contributions he had aside from the pre-production.

Overall:
The show ranges from average to kinda good. It definitely doesn't do anything too offensive to be considered bad but also doesn't do anything too good to be considered great. Also due to its muddled plot direction, the show comes off bland at times. The show has a lot of cool ideas, but they're not executed that well because of the previously stated problems. The show does improve a lot after the first quarter, but it still feels incomplete overall, has a pretty rushed final arc and has a mixed bag of a finale. Overall, I can only recommend this show if you're really into Kamen Rider or if you're really into the villains of this show after watching the first 3 episodes since they're by far the most consistent aspect of the show. While this show isn't bad or even mediocre, there's just far better Tokusatsu out there, and this show doesn't particularly excel at anything.