the show is designed around "sunday funnies" setup, where everyone starts out as stereotype to ensure that an audience can understand the character dynamics no matter what episode they watch. It's similar to an episodic series like say Gumball, but there will never be a change in the show that requires you to go back and watch previous episodes, since any information in a given situation is taken as a matter of fact instead of "you remember that one time - blah blah blah"
That being said, there is character developement, it's just not centered around changing a character and instead is to teach you new information about them. This can make Lincoln seem a bit like a Gary-Stu since he rarely suffers any consequence or is even in the wrong, but him being the audience surrogate and 4th wall breaker does mitigate this.
As for the episodes being stereotypical, yeah I can't argue with that, it's pretty much built into the show, the appeal is more how Lincoln gets from point a to point b, and the sisters also get episodes where they are fleshed out bit by bit, if you want more than that, hold your horses, this show is barely on its second season, even SU barely had any great episodes in season 1.
I would like to see more feels worthy episodes, however I also don't think the show will be steering in that direction anytime soon.