You know, I never really understood the idea that Batman has a "no killing rule." I get that Batman writers have made that a trope in some storylines, since they keep raising the stakes of villainy of his Rogue gallery and make the Joker more and more depraved.
Its a standard rule for most mainstream superheroes, so its not like its a special rule that Batman has that needs a special reason to explain. I'm on board with the Batman "no guns" rule, but a "no kiiling rule" is just a general rule that most superheroes follow. I understand that if Batman killed the Joker, he would save an incalculable amount of individuals from harm or death. But that same question could be asked about any comic book superhero. Spider-man - Green Goblin, Green Lantern - Sinestro, Superman - Zod..... (oh wait, we saw that in Man of Steel....).
In terms of the point of the OP, from what I understand of it, 'not killing' gives moral high ground / pride / doing the difficult path instead of the easy route / avoids the negative psychological consequences of murder, and whether it has any scientific merit. I would argue that it does not have 'scientific' merit. I am not aware of any mainstream (Re: Reported on by major news outlets as opposed to scientific journals) reports that the act of killing has an effect on the brain, neurons, etc. Sure, there have been reports on apparent differences in electrical activity in the brain of 'normal' vs 'sociopathic', etc, but none that would likely fit with the OP question. So there likely isn't a measurable scientific basis for a no killing stance.