How many situations have there been in actual Batman media^[Excluding the ones that ignore the no killing rule, obviously] where Batman refuses to kill someone knowing that doing so will directly cause the imminent deaths of innocent people? Not some theoretical future harm based on an assumption that a criminal will escape and kill again, a situation where subduing a criminal is not enough to prevent them from killing someone and the only way to save a life is by killing the bad guy first.^[The closest I can recall is a cartoon where he and several other heroes had the opportunity to kill Granny Goodness, and then later he had the opportunity to blow up Apokolips and take out Darkseid and all of his minions. The former is a somewhat questionable decision because she can't be arrested and imprisoned, it was a choice between killing her and letting go and the harm she would inflict afterwards is predictable if not immediate. The latter is a more impactful decision, but it's a lot harder to argue that getting everyone out alive and ending the immediate conflict is obviously morally inferior to killing an entire planet full of people (including yourself, your team and the people you came to rescue) just to take out its leaders.]

The argument always seems to be that Batman should kill the Joker instead of capturing him because the Joker will escape again and thus will kill again. Of course, in-universe the Joker's escape is not inevitable. We only know he will always escape because he is a popular villain that the writers will keep bringing back. Batman can't know that. And even with that knowledge the argument falls apart because killing Joker won't stop him anymore than arresting him would.

But beyond that, why is it Batman's job to play judge, jury and executioner? And exactly how do we decide when someone is so evil and dangerous that they should be killed even if they could instead be captured and imprisoned? The whole argument starts looking a lot shakier when we take away the costumes and start applying the same logic to normal people in the real world. I suspect most of us would be uncomfortable with a cop just shooting someone instead of arresting them because they figured they'd end up back on the street at some point, or a paramedic letting an unconscious murder suspect bleed out because they might kill again.

Also, we already have Batman but he kills people. He's called the Punisher. Somehow, despite decades of waging a much more literal war on crime, all those innocent people don't seem to be any safer. Funny how that works.^[Yes, I know, this is applying meta logic again, but that's half the point. No course of action the hero takes will ever succeed if doing so would completely undermine the core concept of an ongoing series. And without being able to rely on some out-of-universe justification to claim that the consequences will be better, it's pretty fucking hard to argue that the Punisher's methods are morally superior from an in-universe perspective.]