He has to endure being reviled as someone who makes a mockery of the law while privately binding himself within the law. You just can't have it both ways. Either you can get your hands dirty or you can't.
And he's picked his fights and drawn his limits. Batman catches bad guys. That's what he does. He doesn't follow due procedure and that is that as far as things he doesn't obey go. He doesn't judge. He doesn't make the laws. The system that he's criticizing by his existence is the police, not separation of powers as a whole.
I maintain that killing someone like the Joker or Zsas wouldn't be murder, it would be a "putting down".
Maintain all you like, legally it wouldn't mean squat. They're human beings, they get exactly the same rights as other human beings.
If you decide to work above the system because its broken, then you're supposed to go the whole hog and make sure they can't escape either.
Well, no, your 'supposed' doesn't carry a lot of weight since you're not 'supposed' to put yourself above the system either.
You can't tell me Bruce couldn't have done the same, if he were willing to bend the rules a bit more.
I don't doubt that if he wanted to he'd be an excellent fascist leader, and I am very glad that so far he's been able to stop himself from it. Incidentally, the sort of scenario you're describing is also why I am so opposed to Tim as Batman.