The system that he's criticizing by his existence is the police, not separation of powers as a whole.
I'm not critizing the separation of powers. I'm saying that crime is rampant in Gotham not only because of a corrupt police force, but also because the legal system is rigged in favour of the mobs and DAs, judges and mayors can all be bought and sold. In which case, addressing only one facet of corruption makes Batman ineffectual.
Maintain all you like, legally it wouldn't mean squat. They're human beings, they get exactly the same rights as other human beings.
I think you use the term "human being" rather loosely here, but in any case, can you honestly see any jury in the world condemning Batman (or anyone really) for offing any of these repeat offender sociopaths? Of course, the jury never gets a say in what should happen to the Joker because he's never given a chance to appear in court.
Well, no, your 'supposed' doesn't carry a lot of weight since you're not 'supposed' to put yourself above the system either.
I'm saying there's no point in breaking the rules if you don't achieve your objective in doing so at the end of the day. Batman going out and playing bad cop night after night in the hope of making a dent in the crime rate is as effective as slapping a bandage on an open artery wound.
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.
This is where you and I diverge, because it is the same reason that I am in favour of Tim becoming Batman - he's more practical and less emotionally fettered by his past than Bruce is, and a LOT less idealistic than Dick. I personally don't see how this makes him a fascist leader, since he's operating under the same sort of unofficial sanction Bruce does save that he's assuming the role of both cop and jailer. But your reservations are actually shared by the rest of the superhero community in my fic, who consequently treat Tim with disapproval because they perceive his methods to be a slippery slope to world domination as well as unethical for a superhero.
I don't want to argue about this ad infinitum with you, since it's clear that our moral outlooks are very different. But just to sum up, what I'm saying is this: Monsters walk among us in human clothing. If they cannot be contained, they need to be put down. One cannot bring order into complete chaos through democratic means. Sometimes, you have to work completely outside the system to right its wrongs. Sometimes, you can either protect your ideals or you can protect people. If you aren't superpowered, it usually means you can't do both. And there should be exceptions to every rule - including the "no kill" one.