I think Batman should be more like Patrick Bateman.
Bruce Wayne has serious psychological issues, but even when dressed as a Bat we never seen him actually act like it.
Bruce Wayne should be all charming superficiality and barely contained rage. He says the right things, smiles at the right times, but you can tell he's barely there behind his eyes. Barely holding it all in.
As Batman he should be as inhuman as possible. He wants to scare criminals but if you've got that tiny bit of human mouth showing they'll all know. I'm talking prosthesis to make him look like a monster, a literal Bat-man, while retaining as much maneuverability as possible. Fake hair, fake fangs, claws. He should look demonic.
His fighting style should also be primarily from the shadows, hidden, taking people out one at a time, never showing more than a glimpse of himself. Heightening panic. He should never just dump himself into the middle of something to fight five guys, because now those five guys know he's just a guy in a costume, when he needs to be a supernatural being in their minds.
He should also be more brutal. Cripple them, break their bones, tear skin off. As long as they don't die, it's open season. We should see him paralyze people on a regular basis.
And that's what I think about Batman.