You can write "no way out" scenarios where he doesn't have much of a choice without just putting a gun in his hand. Heat-of-the-battle shit is going to happen, as much as comics try to pretend it doesn't.
But I atleast wanna believe in a Batman that will try his fucking hardest to avoid it. Because if he is just offing people, Gordon working with him with a bat-signal on the rooftop fucking sucks, and he just leans closer to being the Punisher, but also a billionaire (which sucks in its own ways).
I want a Batman that is informed by his damage and wants to believe Gotham can stand up, vs. just being consumed by it and just gets away with killing who he thinks isn't worth it.
There was an issue of Injustice where, in a vision of an idealized alternate scenario, Bruce killed the Joker instead of Superman, before Joker triggered the event that would have killed Lois and destroyed Metropolis. He knew what would have happened if he let the Joker go through with it, so he stopped it himself. He then turned himself in, served his time, and was judged. This was all just a dream of "a better world" than what ends up happening in that comic, but it atleast displayed a Batman that was willing to be held accountable by a system he wants to prove can work.
I would love that if Batman ended up straight up killing someone extrajudicially, he would turn himself in. But really, DC wouldn't allow that.
Atleast the Dark Knight ends on an interesting notion of letting Batman be labeled a pariah, and be blamed as a fault of the system. DKR follows it up in ways that both succeed and fail, but there is atleast a notion that Batman's existence is diametrically opposed to a system that works.