Look at other parts of life, where do we require that someone cannot be anonymous (warning I am a Brit, things may differ where you are)
If you publish something, eg a newspaper, a handbill, a poster (on a wall), these should all have the name of the publisher on them. This seems reasonable, you are saying things that many people will hear/read. If it is libelous then the person being defamed should be able to seek correction or sue you.
If you sell something: the name of the seller should be known, so that if it is not as advertised the purchaser can seek redress.
If you read a newspaper, handbill, wall poster then it is reasonable that you do so anonymously.
If you buy your lunch or a new shirt, you do not need to say who you are. (Large purchases, maybe)
If you talk to a friend in the street or on the train then you do not need to tell those around you or fellow passengers who you are.
So: does this mean the loss of a/c on slashdot ? If you are libeled by an a/c what redress should you have (if any) ? These are the sorts of questions that should be debated. But the loss of privacy in everything - 'No', the loss of privacy in some situations 'Yes'.
Note that you not liking something that someone says is not the same thing as being libelous - if you really smell, get a bath don't sue me for saying so!