I would love this!

GW2 handles this in a pretty awesome way. You can befriend anyone, on any server, and you can send them /w's and even hop over to their server as a "guest" to do things with them.

So much of our time is spent in dungeons and raids with random people that we will probably never get the chance to speak to again. As others have mentioned, this encourages people not to bother talking as "what's the point"? Also, I think people are more likely to turn into jerkfaces because they know they'll never have to deal with them again.