He's just never stretched himself at all and your theory about why makes sense. I believe he's publicly said that his plan was always to be the most famous and successful, so of course that would stunt his artistry.
What that leaves us with is a guy who really only plays two roles:
Couple that with the fact that he's on about a 20 year run of mostly awful performances and movies, and I'm not even sure he's anything above a serviceable actor. He's wholly dependent on the audience being a fan of his schtick.