That's something that bugged me too Locutus. In Batman Begins, much was made of the fact that Batman was more useful as a symbol than as a man. But if it's known that he's murdered cops, then how powerful of a symbol is he?
Right, that was always the chief thing that separated him from run of the mill vigilantes and copycats - his refusal to kill. It was the one thing that allowed him to be accepted by at least some of the police and the people despite operating outside the law. Now that's gone.
I suspect that won't last for very long since the people of Gotham kind of know the truth about Batman namely that he's on their side.