I don't think so. Look at World of Warcraft, for example, most its endgame is PVE - doing heroic mode dungeons, raids, scenarios and dailies (I personally hate the last one). Although most the F2P MMO's endgame is... inexistant. You only reach the last possible level and there's nothing else to do, regarding some quests you left behind (Perfect World, I'm looking at you).
Obviously, some games (such as GW2) have PVP as endgame, but these MMO's are focused most of the time on PVP.
I think that's all. xD