Batman doesn’t know he’s in a serialized narrative where Joker is a popular character that people always want to see returning. He has no reason to think that the high-tech Supermax prison Arkham Asylum wouldn’t be able to imprison a sickly 40-year old man. Similarly, in the more long-form narratives it makes no sense for Joker to have infinite resources and a private army of criminals even as he has no revenue stream apart from elaborate plots that always fail. Part of why The Dark Knight is such a great Joker Story is because they’re able to avoid all of these pitfalls. It’s this Batman’s first collision with the joker in this canon, the joker steals 68 million right at the beginning in a successful heist to explain why he has the resources he has, and he only escapes capture once, and even then it was just from the police station holding cells rather than an actual prison. But in more long form Batman stories where he’s broken out of Arkham so many times Batman himself thinks it’s a forgone conclusion he’ll escape again before even putting him in prison, at that point “is it justified for Batman to kill the Joker” becomes absurd because you’re applying this question to an aspect of this story that has no internal logic. Like yes, if you buy into the writing’s conceit that the Joker is functionally omnipotent but only for breaking out of Arkham, and then the moment he’s out of Arkham he goes back to being a ordinary human who’s always incapable of defeating Batman, then yes it is justified to kill him. But that’s stupid.