Try playing a D&D game where one player is level 20 and everyone else is level 1. "Hey, we're all on the same side so it doesn't matter"... no.

"Dave paid the DM $50 so he gets the level 20 character. That's just the way it is, you can like it or leave."

Differences in player power will break cooperative games just as much as they'll break competitive games.

"Okay, so here's the kill stats. Dave: 1,422 kills. Sally: 3 kills. Bob: 4 kills. Lacey: 7 kills. Good job working together everyone!"