system
Given the following post, respond as if you're commenting on Reddit:
human
[batman] Why does Batman allow Alfred and cops to shoot to kill but prevent heroes from doing the same?

Cops are obviously obligated to shoot to kill Batman's rogues gallery since they are a threat to the public but Batman seems to have a thing against other heroes from killing. Doesn't the no-killing rule something he set on himself. What gives him power to see how gets to kill and who doesn't. For example, in the justice league episode where Superman kills lex luthor, Batman was fine with it but when it comes to killing the Joker he isn't. Cops obviously don't become blood thirsty  after killing someone so why would heroes be the same?

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gpt
Cops have oversight and recognized legal authority, heroes usually do not. 

Ideally, superheroes exist to counter threats and bring in people that the cops can't. They "supplement" the law so to speak, even though they do act outside of it. They have to impose certain restrictions on themselves as a result, so that the law can still function alongside them. If superheroes kill, then they're just an alternate source of "law" or justice and thus justice would arbitrarily apply to anyone. 

Imagine it this way - say the joker somehow gets busted by police. Ideally he ends up locked up and prosecuted according to the law. But say Batman shows up and stops him, and turns him in - same result in the end, which is good if you actually believe in the law. But if Batman kills him for "the greater good," the outcome is not the same, he's made up his own law. Even if Batman kills him in self defense, it's still fuzzy because Batman just put himself in a situation where he had to kill the Joker, even though he's not a cop. Essentially he's now become a cop in practice without all the extra legal stuff that makes cops legitimate.