His wealth is an asset, no doubt, but in the end Batman is still human and is only slightly less vulnerable as a random dude. Even when he fights ordinary criminals, Batman is still taking severe risks. Batman without his wealth, is basically Daredevil.
Superman, Spiderman, the Flash, etc. don't take the same risks and don't require the same planning because they can just rely on their superpowers. And the only interesting enemies they have must have superpowers, as well.