That's what makes Batman 'good' and not just a vigilante. Kids lock onto that notion of good, and everyone I believe quietly likes the idea of their hero nursing qualities of potential reform/ forgiveness. Even if the villains have been doing their schtick as vehemently as Bats, that's the yin/gang of Gotham City.
The Batman should not kill. Even inadvertently. If he does, its to foes he knows can survive. This edgelord Frank Miller/Goyer writing of Batman manslaughtering and neglecting to save his film villains needs to end.
Fucking comics. Not all of it needs to make 100% logical sense, that's what helps make it fantastical.
Batman kills any extreme criminal in Gotham. Bat family gets real jobs and starts up Facebook pages. Damian starts shopping at Build-A-Bear. Arkham Facilities put supercriminals' shit up on Ebay.
Bruce marries, invests in his company, plays with Ace every day, and Alfred is finally in such a senior state that Bruce passes the time by caring for him.
Duke is head of the Black Lives Matter/Black Culture Centre in Gotham.
Dick is a gigolo.
Like, how fucking boring? How fucking not Batman? Where do you go if you let Bats kill? Psycho town? What's the finish line for that?
MAN OBSESSED WITH BAT KILLS ALL EVIL IN GOTHAM, RETURNS TO NORMAL LIFE
Does someone like Bruce Wayne deserve a normal life, ever?
No. He's marked by flaws, ego complexes, power tripping, an addictive need to know & control, and fury. We know he's imbalanced, but if he starts killing his co-operation with Gordon and the whole 'good guy' dynamic of the Batman is summarily trashed. Supes would actually incapacitate him, instead of nuancedly holding back. He wouldn't plausibly be allowed in the Justice League.
Fuck, even Thomas Wayne wasn't approached by fucking shit until World War 3 was about to end everything. 'Cause he was killing. He was alone. He was an alocholic. Killing makes the characer feel hollow.