This is the case in Guild Wars -- when you roll a character in that game, you choose it for PvP or PvE, and there are certain things you can only do with each. And even Blizzard is heading this way, believe it or not: with the debut of the Arena realm this weekend, some players are already clamboring for characters that they only play Arena with 24/7.
Are we really ready to split the game into World of Warcraft and Warcraft Arena? There will no doubt be a lot of players who want to continue to play their characters in both PvE and PvP, balance be damned. But if Blizzard is as committed as they seem to be to balance Arena as precisely as it needs to be balanced to turn it into a real e-sport, they may have to eventually make the jump and separate the two games completely.