I think the key point is that Batman is about fear, and fear as a weapon is kind of like a hand grenade. It's not a precision instrument. Batman scares people by design, and while there have been moments when he seems to regret that, it takes a back seat to his one-man war on crime. He chooses to play it from the shadows, but the price is that he becomes the boogeyman whose motives may seem to be on the side of the angels, but where you can never be quite sure.
All that said, it also seems that his ambiguity ought to be played out more. There are times when criminals seem to know he won't kill them, but it would seem to me that it should be a lot less certain. As has been pointed out, I'm sure he'd be blamed for lots of things that he didn't actually do, and he's also not the type who'd work very hard to counter those perceptions since it would be something he could use as a lever to make criminals more afraid of him.
Superman and Wonder Woman play much more publicly, and Superman specifically has gone into PR to ensure that he's not viewed as a threat. I remember Lois & Clark talked about how he finally agreed to merchandising on the condition that the bulk of the proceeds were donated to charity, and I recall that was lifted from the comics. Wonder Woman also has her specific brand of community outreach (which, I'm sure, angers a portion of the population just as it appeals to a different portion), but the point is that she also has a visible, public persona.
Also, I'm not sure I'd take anything in All-Star Batman as canonical Batman. That series struck me as Frank Miller seeing how much he could get away with more than anything else.