Though it can take practice, we can and do make use of anonymous messages. It is merely a new "mode" of communication, and it gives rise to certain types of communities. However, anonymity must be consensual for it to work. Law enforcement will still come after your identity depending on what you say, and that is a case where the consent is broken (or never acknowledged according to them). Messages become drive-by shootings, and this has an effect on the exchange.
Also, user names are not the equivalent of anonymity. On HN, karma is a feature of each identity, and baggage can be attached just as easily. And if someone says anything interesting, we can read their other comments to learn more about them. As we read more of what they've said, their user name will begin to have a unique aura. Now if we happen to read a new comment and recognize the name, it will ring a bell automatically, and we will already be working with more information than what was included in the utterance alone. At this point, we are not forced to consider the message on its own. We are working with identities that just may or may not be real.
It's kind of a mess, and it's really not fair to anyone.
Anyway. Yes, anonymity carries its own baggage. But it's a separate sort of baggage, out there to be assumed by anyone at any time. There's a long and proud history of anonymous authors affecting politics or writing biting satire that would have been impossible without anonymity.
It doesn't break the message to lack identity. It forces you to consider the message on its own, stripped of whatever cultural context or baggage you might attach to it.