The man regularly outwits far more supposedly cognizant opponents including Batman and Lex Luthor, who are canonically recognized as two of thr smartest people on the entire planet.
Edit: I’m not saying insane people are stupid, I’m saying that Joker’s mental illnesses are pretty obviously behavioral, they don’t affect his perception of reality. He’s perfectly capable of understanding what he’s doing and how it’s wrong, in fact his character almost doesn’t work if he doesn’t, he just thinks that it’s all hilarious anyways. That’s why I said he’s not insane, he just pretends to be, because he’d be fit to stand criminal trial as fully competent and cognizant of his actions.
Well I mean that not how the writers who control the story write it but as far as realism there is a fair amount of mental illness that actually correlates with higher intelligence rather than the opposite. One of the hard parts of dealing with schizophrenia is they can be highly intelligent and manipulative despite their crossed wires reality wise.