Honestly, in anything resembling a realistic world, someone would have done just that. Especially if Joker's a cop killer, someone would have put a bullet in him and sorted out the paperwork later. Or he'd have met an end like Branneck, done in by a vengeful loved one of one of his victims.
Even Batman himself is likely to see the overwhelming need to make an exception for a man who has continued to kill and menace so many while proving so immune to conventional consequences. And he's smart enough to do so without his involvement being known, though even if it were I find it hard to imagine anyone giving him any grief over it.
There should probably be a special medal waiting for whoever kills the Joker, given his history.