Let's be honest. Sometimes we like a drama and can't even figure out why. I had this with Another Miss Oh, Go Ho's Starry Night and, to some extend, with Heirs. I just started watching and couldn't stop, but also couldn't quite understand or justify liking them so much when I finished.  
Any shows like that?
Same thing with love o2o and devil beside you for me . There wasn't much of a storyline yet i liked these shows so much that i  binge watched them. I also liked the heirs when i was watching it .  I just can't figure out why
Padam Padam is one for me because i don't like shows with tragedy but i loved the show, the characters, the acting, the feelings it generated, the bromance, and I just want to watch it again.  

 
I second Love o2o though it's a chinese drama.

Stranger (2017) korean drama, is very good imo.

There's a lot more I binged but can't remember them right now lol
Now when I think of it, Marriage, not Dating was another drama like that. The female lead was kind of pathetic, the male lead started as a jerk, the secondary female lead was plain annoying and the secondary male character couldn't act to save his life :D On top of that, the story wasn't really great and the other characters were flat. Despite all that, I actually binged watched it and had a lot of fun while doing that. I can't logically explain why. Maybe it's because it was light-hearted?
I can always explain why I liked a drama even if it's not my usual type. I loved YWCFTS but romcoms usually aren't my thing at all. I actually started it thinking I wouldn't like it, but I love high end fashion and wanted to watch for that. I binged watched it despite the romance because: I loved the lead character and found her relatable, the fashion was great, Shin Sung Rok's acting made me fall in love with him, there were other plots outside the romance, and the humor was my type.

Who Are You - School 2015 is a drama where I felt took a turn for the worst, but I loved too many things about the story, the characters, and the acting so I was sucked in despite how it was progressing.

There have also been dramas I've watched in the past that aren't objectively great dramas but were really entertaining and a light watch, so I enjoyed them enough, like You're Beautiful.
Love Exposure lol I honestly don't even know why
Jealously Incarnate. I love Gong Hyo Jin, her acting is so good. But Lee Hwa Shin was such a jerk. I felt sorry for her that she liked him. He became a better person after bad things happened to him, but he was too cruel to her before. I loved the drama but god, I dont know how I managed to finish. I also hated Go Gyung Pyo character, and there is one point of the story that she doesnt know which one she loves... that made me angry. At the same time I liked the different views in this I was almost crazy at the end! Love and hate at the same time. Maybe will rewatch again when I feel my life lacks some emotion.
Innocent man idk have idea why I love this drama lol
Noble My Love, I have no clue why, but I couldn't stop watching it and can re-watch it again and again too.
I second Noble, My Love. I don't like the rich man/poor girl romance. And in this drama the guy is overly possessive with the girl in an unhealthy way. Of course the romance between them it's also full of cliches. But despite all that, I really liked the drama. 
The Heirs, Hwarang, and Playful Kiss