The question of ‘does Batman kill’ misses the the much bigger moral question
However, through the years this hasn’t necessarily been true. In, Tim Burton’s 1989 Batman, the Dark Knight doesn’t go out of his way to kill the bad guys — but he doesn’t agonize over the fact that he definitely offs a couple.
You might chalk that up to the rather inconsistent relationship both Hollywood and Burton had to the source material. However, if you look even further back, the when the character was first introduced, Batman killed all sorts of people. Sometimes in rather brutal and outlandish ways. (Such as slowly choking a mental patient to death as he hung from the batplane.)
The real quandary has never been does Batman cross the ethical line of killing people, but the much bigger, far more nebulous question of “is the violent Batman a force for good?” and “is this vigilante who acts outside the law just?” The ethical rule of no killing is just a small part of this larger moral question
On the surface, the answer, of course, is no. He isn’t. He’s a near psychopath driven to vengeance and violence by his parents death, acting as judge and jury in his quest for justice. The only way this works as a good guy is through the fantastical lens of pulp storytelling.
That’s where the “no killing” rule comes in. In a bid to answer the moral question of “am I just?” with “yes,” Batman has created a (relatively simple) ethical code: He will not kill.
It’s notable that the code is actually stricter than the one that the police follow. Where a law officer can employ lethal force in numerous situations, Batman tries to never allow himself to kill, even in self-defence.
For better Batman writers, this adds a level of nuance to the character. Batman knows he has to set a higher ethical standard for himself because the lack of checks and balances on his extra-legal activities have a much higher chance of slipping into injustice. He doesn’t trust himself with the power.
Weaker Batman writers use Batman’s lack of killing as a way out: Of course Batman must be good because he doesn’t kill. The the swathe of destruction (and permanently crippled thugs) the costumed millionaire leaves in his wake are justified with a hand wave.
This quandary is tackled specifically in perhaps the most important Batman story: Frank Miller’s The Dark Knight Returns. In DKR it’s pointed out repeatedly that Batman is really doing a lot of damage. He’s all but breaking the people he fights. Yet the police, the public and the reader are assured that he still isn’t killing, so he must still be a force for good.
In the book, Batman breaks the Joker’s neck leaving the clown immobilized and the Joker twists just a little bit more, killing himself.
Is this meant to mean that the Joker has forced Batman across a moral line? Or just that the Joker has made it seem like Batman is no longer just? Or is the Joker just exposing the lie that the “no killing” rule perpetrated: namely that Batman was ever morally good.
Like most great works, Dark Knight Returns is ambiguous on these points, letting the reader mull their own answers about justifying Batman. (This ambiguity was, perhaps, not the intended meaning from by the author, but it’s nice that we can ignore him.)
Which, of course, leads to back to the start point. The question isn’t “does Batman kill,” but “does a rule about killing make the violence he inflicts moral?”
The important part is that Batman himself grapples with the problem, hence the rule in the first place. That’s what makes the character interesting.