I think there is a difference between someone who is defeated and broken, and someone who has just turned into a cynical IDGAF asshole.
Seeing his whole academy up in flames and not being able to save the students that were slaughtered by your own nephew I think would mess with your head for sure. Kylo Ren did basically leave him defeated. I also don’t think there’s a distinct difference where the two traits can’t be mutually exclusive. Luke’s defeat at the academy would lead to that cynicism. “Ha! The great Jedi Master Luke, the legend himself, couldn’t succeed in restoring the Jedi Order!” and “The Jedi teachings have led to the galaxy’s greatest threats, so what’s the point?”
Granted, I’m not saying this was written well in TLJ, in fact, they tried to sell Luke rather poorly, but I think the concept was great.