What I like most about this is that it would form a sort of invisible reputation quietly affecting your odds of getting a fast queue. If you're a fabulous hunter or mage with whom cross-server tanks had a great experience and who got "friended" a lot, you could bypass the usual wait if one of them queued at the same time you did.
There's even a cogent point here about being able to affect how you experience content: If you only "friend" tanks who pull like a ferret on meth, you could increase your odds of landing a fast tank in subsequent runs. By contrast, if you're a jerk player who's a hassle to be around, all that other players would have to do to keep your wait times unchanged would be not to friend you.
I agree with Heartbourne's point that this isn't a perfect system and it could be problematic for newer players down the road. "New players tend to be DPS," he points out, "and if all the tanks and healers get gobbled up by small communities, it could leave new players high and dry." But I do really like the idea of a little self-organization through the dungeon finder, and when you think about it, it could also yield some interesting data for Blizzard. Is there a particular class of tank or healer that people are more likely to "friend"? Which DPS get "friended" most through the dungeon finder? And is this the sort of system that should apply across all of your characters, or just one?