The only difference is that he acts out his violent fantasies against criminals instead of the general public.

I think this glosses over a bigger difference that lets his character off with a little less shit on him than he deserves: the only difference is that he can afford act out his violent fantasies against criminals. If beating up criminals paid the bills, I’m sure more of the criminals would do it. In fact, it’s so obvious that crime-fighting isn’t lucrative in Gotham, evidenced by the astounding number of dirty cops. The big baddies punch down on the general public because they can squeeze out money that way. The only reason Batman continues to get away with cosplaying as a villain is because the general public lets him get away with it.

Batman will have billions no matter who he beats up and he can afford privacy and security in his private life. If Batman tried beating up a villain and then went home to find out that someone killed Alfred to send a message and that Bruce Wayne couldn’t afford to feed himself, I’m sure it wouldn’t take long before his inner rage unleashed on some innocent bystander and he’d realize that beating up anyone feeds his violence addiction and that stealing money and food feeds his hunger.

And let’s not forget: these “criminals” are mostly people who were ostracized and desperate before getting caught on some charge that landed them in Arkham. When they were finally released, they were even more radicalized, unemployable, and destitute. If crime is their only perceivable career path, they can’t be faulted for that. And all of this begs the question: what kind of fucked up economy exists in Gotham that “villainy” is the second richest employer behind “self-employed billionaire bare-knuckle boxing bastard.”