He can continue to be Batman, but one who is morally compromised and, hopefully, repentant. I do not find that entirely objectionable.
That's fine; no one is required to have my experience.
It would underpin a scene such as that which opens The Killing Joke, where Batman seeks to divert from a path trodden with The Joker that leads to mutually assured destruction, a different kind of poignancy.
I have high hopes for Affleck's directorial effort, as I thoroughly enjoy his films--but if I'm honest, I half expect Snyder will have Batman continue killing his opponents in Justice League because it's
totally awesome and/or
completely ballin'. In which case, such a scene in Affleck's Batman film would read as absurd.
BVS is sufficiently vague as to whether killing still fits within the
redeemed Batman's acceptable methods, and Snyder's comments on the matter run more along the lines of "I think it's okay because Batman's killed in these other stories," as opposed to "I think it's part of a larger narrative about the character in these films." I try not to hold creators to what they say when they're put on the spot in interviews, because it's rare to get a complete and truthful answer in those instances, but I do, honestly, believe that he doesn't think too much about these things.
He is, after all, the guy who said Batman "kills all the time" in The Dark Knight Returns. Unless one believes that the entire work is satire of Batman's history of flip flopping on the matter of killing (and that he guns down mutants with
real bullets at the trash yard in a story where he also, quite centrally, claims not to kill), the position that he "kills all the time" in The Dark Knight Returns can only be understood as a fundamental misreading of the text.
Or, more simply: I don't trust Zack Snyder to tackle this material competently.