There is so much lore behind Community and Chevy Chase. My understanding is that Community was supposed to be his show, where he was the good guy and was the main protagonist, not Joel McHale. (You sort of see hints of this in the gas leak year.)

As the series went on, it was clear that Chevy was annoyed about their long hours, shooting schedules, etc. TBF to Chevy, Dan Harmon made every episode into a movie that required a lot of shots, something that made him disliked by network executives. It's why he got fired over Chevy in season 4.

What every executive failed to realize is that these "movies" were absolutely awesome and that's why the fans love the show. They were smart, funny, and gave you a sense that they weren't taking things seriously.

In the end, the show was better without Chevy.