I would have to disagree strongly that the public would welcome a superhero who was willing to kill. Look at how many people already oppose the death penalty and then explain to me why those people would suddenly be fine with some vigilante in spandex serving as the executioner.
That said, I think that in the comic book world it would be alright for Batman to take that extra step only if it was necessary to save someone and there was no other way. Making Batman into a killer is one step away from Punisher sloppiness. Batman has finesse and style.
