He's almost as unrealistic lol thats true, well, depending on the writer.
When they did Batman's Knightfall story arc, when Batman was fighting arkham villians and escapees and eventually Bane, you were looking at a far more realistic version of Batman. He would tire, didn't have everything planned out, people out-fought him, he critically injured himself, etc.
He wasn't a genius electronics tinkerer or an invincible warrior, he was a tough son of a bitch getting put through the ropes who finally got beat. None of it is realistic (a man in a bat-outfit fighting people dressed as question marks) but at least there was some coherence there. It was a little more consistant with who Batman is supposed to be, a detective crime-fighter with unrelenting drive and MMA skills.
The issue is, when Batman gets on board JLA storylines, they need him to be able to do something. You can't go up against world beaters like Darkseid with Batarangs and a fast car.
So they turned him into a Cap America level peak human and added some Reed Richards/Tony Stark level tech genius - because Batman is DC's #1 character and he can't play second fiddle to Green Lantern, or the Flash, or..booster gold.. in the JLA. If he's gonna be in the JLA he has to be something special, so, they made him this crazy "always-win" level human.