Personally, I'd never tolerate being stuck with a "random" teammate.
Why not? That sounds like a lot of crazy fun.
There's lots and lots of players that I'd never end up on the same team with unless it was random.
It's fun, but not in a competitive setting, in my opinion. It almost erases the team work element--players would be rewarded less for specializing in something. I suppose you could argue it'd encourage versatility and quick adaptation to a new partner, and yet without a headset, I'd say no thanks.
Well, what if... You're on your own bracket, your teammate changes periodically. I think that introduces a bit more competitive spirit.