I know there are about work etc where people grow in their personalities and end up being better at what they do, but I mean like for example a soccer team fighting from the bottom to the top, or something like the Japanese drama "waterboys" - just 5 boys training together and fighting for their dream which is to perform synchronized swimming. Waterboys is full of many heartwarming moments, bromance and romance. To see how they overcome all the hardships is such a joy.

Or why not a group of people opening a new restaurant? Say they buy a dirty place, clean it and aim for the top. Overcoming hardships, fighting for success, and around that they can of course have all kind of side stories like romance, bromance etc. There was a little of that in Pasta and Coffee Prince but it is still not the main story of the drama.

There are many Japanese dramas like this, "sports com" as they are called in Japan, two examples are Waterboys and Suikyuu Yankees, but I have yet to see one from Korea. As korea makes the best dramas in the world, I am sure they could make a story like this so damn good. 

Why do you think you don't often see this in Korean dramas?

try Bachelor's Vegetable Store - dude starts a vegetable store and turns it into a chain - true story
Page Turner - kids trying to be excellent pianists
Beethoven Virus - amateur orchestra tries to make it big
Night Light - poor woman has excellent business woman as mentor and tries to learn how to succeed
Sassy Go Go - cheer leading team fights for their right to exist
you should try Dream High, tells the story of six students at Kirin Art High School who work to achieve their dreams of becoming music stars in the Korean music industry.
Yeah, I was about to say there are lots focused on performing arts and the like: What's Up and The Musical come to mind.  Also Tomorrow's Cantabile.  I'd also add Taereung National Village for a sports-themed drama, but since it's focused on athletes in individual sports, maybe it's not exactly what you're looking for.

The only other thing I can think of is Awl.  Much darker and less clear-cut, but still a group of people banding together to fight.

Not sure why there aren't many dramas like that from Korea.  They save all those types of stories for movies, I guess.
Over The Rainbow : the struggle of group of friends to succeed in the music industry together
God of Study : it's like dragon zakura
Heading to the Ground 
and  yeah there's not that much in korean drama like it's in j drama