Some times, I want to see the Joker or some other crazy murderous non-powered super villain in Texas or at least the South where the death penalty and civilian gun usage is more prevalent. Or at least a line saying why they wouldn't.
"TEXAS?! I may be crazy, but I'm not stupid. I use one of my little toys for some fun and next thing you know even the soccer moms are forming the posse to lynch me. No thank you, I'll stick to the coasts."
Why the sponge?
They put a wet sponge on top of the soon-to-be-executed guy's head, in order to make the execution process faster, so he won't suffer any longer than needed. You know, water + electricity.
Why did Gordon remove the sponge?
Cause the Joker tortured and handicapped her daughter, Barbara (Batgirl).
to be considered insane by the court you have to prove you where not in complete control of your own actions, like having a severe psychosis or compulsion, something normal rehabilitation couldn't fix
a normal mental disorder wouldn't be enough
joker is a sociopath lacks (normal) empathy a sadist enjoys hurting others and a warped view on society but he is still theoretically capable of leading a crime free life like a lawyer with some bondage on the side
while someone like the riddler could make a compelling case for pleading insanity
also Arkham asylum is a mental institute not a normal prison pleading insanity isn't a get out of jail (free) card (in the batman universe)
While the insane can't be executed they can be put into an asylum, for batman villians that would be Arkham Asylum. But if that Asylum was like near every other American Asylum in history, then the joker would be dead in a month. Either from testing, disease, outright murder or even lack of basic human amenities.
I don't think anyone would bat an eye if the joker received just one too many electroshock treatments. That's all to say if Arkham Asylum was like the asylums of old.