One of the things that's always bothered me (and perhaps many others) about Joker is that he is never really shown to display signs of mental instability aside from his love of killing people in fact he's more than like a psychopath with sociopathic and narcissistic traits but he often displays traits that go against those diagnoses. So it's hard to pin down what he has. My personal belief is that he has a multitude of mental disorders and they all function in a way that make it hard to really diagnose him however he has moments where he's lucid (not crazy or as crazy) but still lacks basic morals.
However if only to justify his constant being sent to Arkham I think maybe there should be a story line where it's flat out shown he is to some degree not sane not just having a lust for killing but genuinely not very stable. Like something that plays to him not being able to remember his own origins for example he's in the middle of a robbery or massacre(possibly a shoot out with GCPD) and he starts spacing out and rambling at a critical time giving even his goons the chills and even doubts as to whether they should be following him. Like he starts calling people by different names and acting like he's somewhere else and to avoid any clues to his true identity their could be serious inconsistencies and what he says could also be lines from famous books and movies. Pretty much something like this