This has been on my mind for a long time.

Yeah, I get that you can't execute someone who's insane, but insane or not no society would ever tolerate this mad man. Once he has proven that he can't be cured or contained, the populace would demand his execution. I'm not saying Batman should do it, but is it believable that the citizens of whatever state Gotham City is in would allow this mass-murderer to continue his rampage? Has this issue ever been addressed?

(I'd like to see a Nexus crossover in which Nexus arrives to execute the Joker.)