I think it is not so much about realism but about consistency within the comic book world. I think the Batman character does play the "normal human" card to some degree. This is the first I heard anyone say that he knows every martial art. In the older comics I have seen I don't remember Batman doing fancy monkey style kung-fu or capoeira moves (ok, he knows them but doesn't use them right?) Anyway, I think just a bada** with a vendetta, detective skills, money, devices, and a secret lair is enough.
That's what I was saying about Hawkman, than found a way to make that character's fighting ability consistent with the story world.
I like Moon Knight better. He got beat down by a Vietnmam vet in a black knight costume in Moon Knight #25. An almost regular guy in a mysterious costume getting beat down by another regular guy in a mysterious costume.
Someone mentioned this as being a difference between Marvel and D.C., Marvel tries to have explanations for everything, even if the are hokey comic book explanations. Not necessarily a worse thing about D.C., you just have to suspend disbelief that much more. Star Trek vs. Star Wars.