The Greater Internet Jerkwad Theory:
Normal Person + Anonymity + Audience = Total Jerkwad
As TheGratefulNet suggests, anonymity is very important. At least in the sense that we value intellectual freedom. Sometimes the quality/range/expressive power of the discussion improves too, so I guess we need it as a comunication tool. I don't know that we NEED tons of anonymity to survive as a species, but it does seem like one of the more enlightened human rights and a good thing to try to preserve.
For now, we have plenty of technologies and forums supporting some degree of anonymity, and I don't see them going away just because Google+ landed on the individuation side. Bad news (for + users): Google+ will lose some userbase and some amount of the good things that anonymous communication can foster. Good news (for lovers of aliases-based communication): some other, less-omniscient service will get a market opportunity they wouldn't have had if Google+ allowed aliases.
FWIW, I have a + alias-as-name and will probably drop 'em like Friendster if they make me change it. I already have a RealIdentity-style social network. (On Facebook. For now. Can't wait to try the Great Opensource Distributed Social Network that I know one of y'all is going to invent.)