OK, if "not playing minecraft" = "stone age", I'm more like, oh, Australopithecus. Still, I am totally for each player having that /ban ability. You're being afraid of your own imagining of what people might do with that kind of power, which is (I think) exactly where government comes from. This "minecraft" is a game; it's a fine way to find out what people actually will do, and nobody gets hurt (except virtually).
It's possible that, since it's a game, people will "kill" much more freely than they would really kill in real life; otoh, since it's a game and /ban = game death (not real death), it might scale.
Only one way to find out, guys.
I'm curious as to how these "griefers" might alter their behavior knowing that anyone could ban them, as opposed to what I imagine usually happens: waiting until enough players have expressed enough annoyance that "God" sighs, puts down His Cheetos, and bans them.