None of those are anonymous in the face of internet surveillance by entities like the GCHQ or NSA. They are superficially anonymous (or pseudonymous, which isn't the same thing) from the perspective of other users interacting through the intended public interface.

It does if you want people to talk openly, without guarding every word for fear of giving away sufficient detail for someone to be able to identify them. And simply because a lot of people will be unable to trust you if the communication is monitored.

Err this is about a constituant talking to their MP you can not not anonymously lobby and MP

Why not? Lobby your MP, have identifying details removed from the public record. We do it with all sorts of records with confidential or secret details.

Partly because of the rule that MPs are only supposed to deal with their own constituents. Therefore they require your name and address on communications...