Joker's very animated in the comics. Crazy homicidal maniac hellbent on chaos. It's quite fun to watch him go.
You're missing the point of him then, he's a character built on obsessive principles... but the principle is Dark Humor with Murderously Comedic Timing. He's "The Professional", but he picked a fucked up artistic medium to paint. There's small hints of it present in the films (like a fire truck being on fire), but it's not on par with how much of a Psychopathic Prankster with a love for puns can be taken. It's led to many situations where Harley's felt ignored over his constant plan-making.
The point about Joker is that he's supposed to look affable from a distance while being pants-pissingly scary in person.
I got into Batman and his villains a few months back. They are very interesting from a psychological stand point and they have good, believable backgrounds and reasons for doing what they do. There's a whole book talking about the psychology of Batman, his villains, and crime which I read and thoroughly enjoyed.
Check The Animated Series from the 90s then.
They obviously depict mental illness since most of them have issues.
Ohhhh yeah, they love doing that for their Rogue's Gallery, and arguably some of the good guys too (Batman PTSD is something Elseworld authors love).
Clock King's issues with OCPD are pretty spectacular, Calander King's OCD is strange, then there's The Ventriloquist (MPD + Dependency), Two-Face (MPD based on self-persecution + fear of taking chances, obsession with duality and fatalism in a black & white way), The Creeper (Mania), Ra's Al Ghul (Narcissism), Catwoman (Kleptomania + Thrill Seeking), Mr Freeze (Depression), Poison Ivy (Xenophobia... with plants being her people), Mad Hatter (Obsessive stalker with Magical Thinking tendencies), the list goes on.
Arguably the one who's the least blatantly disordered in one direction is, ironically, their craziest person (The Joker). He's used his collection of stories and quick wit to drive some of the staff insane.
The mentally insane go to Arkham Asylum and leave after serving their terms or they escape.
Blackgate is where the non-crazies go, like when Batman fights The Mob.
It's also where a lot of henchmen are placed when their ringleaders are in asylum. There's been some iconic henchmen over the years.
They have interesting personalities like The Riddler, suffers from obsessive compulsive disorder, who can't commit a crime without leaving a riddle. The clinicians in the story themselves diagnose them. Not all the criminals are insane, though.
They've tried to write his riddle weakness out of him a few times, once where he was leaving the riddles without his own knowledge, and another time they retconned where it was because "Brain Tumor".
There was also a few comics in it's darker days where Riddler took Bane's steroids and went a little crazy, and an Elseworld or two had him as a detective.
My favorite villain though? James Gordon Jr. Son to commissioner Gordon. Jim Gordon quickly realizes his son is a psychopath. He'd kill animals and take them apart. He was also suspected of killing his sister's friend for teasing him(He did it, but they can't prove it).
He's featured in The Batman Who Laughs, too. He's post-villainy at this point and just "wants to get better" without fully understanding his own issues while also denouncing his gifts in criminal investigation, and ultimately has to feed his issues and drop his medications in order to be helpful in saving people's lives. He's like the journey of the main character in Red Dragon/Manhunter, except his journey's in reverse.
I don't care that you most likely enjoy him because of projection, he's a well written character.
Stories and characters with actual depth is something I never expected out of Batman. I'm glad that someone gifted me the book that opened me up to it.
It's a journey decades in the making.
If you want more source materials I love the stuff.