Batman going "wrong" isn't impossible, or implausible. Owlman is fun (except when they show you how much of a vicious creep he, naturally, is), and I've had enormous amounts of fun with the idea, from a Bruce Wayne who kills to one who built his own prison/asylum under the Batcave. You can even break the current Batman into something worse.
But you have to do it plausibly, and the end result has to be consistent with who he is. These Batmans definitely aren't; at least so far, they aren't shown as Bruce Waynes who went through very different lives, but rather as near-canonical Batmans who had a Bad Day (which is a very Batman thing to happen) and responded to it in an overly dramatic (also a Batman thing) but not Batmanish way.
That also goes to the core of my distaste of Injustice. It's not that I dislike dystopias where a canonical Superman kills somebody and then takes over the world (ah, A Better World, what fun we had); I dislike dystopias where a canonical Superman kills somebody, takes over the world, and starts behaving like a petty, insecure, sadistic tyrant. (I also dislike Injustice in that the worst possible outcome *always* happen; there's a difference between horrendous tragedy and a sadistic universe.)