If Batman was real, he'd have the opposite effect that he wants.

If Batman was real, and he didn't die or get arrested his first week of activity, and if he was as badass and hyper-prepared as he usually is, tough guys would constantly be trying to fight him.

There's a wrestler, Paul White, who is like seven feet tall. And he got into legal trouble in the 90s when a drunk guy felt intimidated and decided to pick a fight with him at a bar. That would be Batman's entire career, with tough guys feeling fear and immediately trying to attack him as a result to prove that they're "not pussies".