Didn't it all start, and become a tradition/common procedure because of security concerns? I mean, you are saying things about yourself and your property and just about any criminal could easily go and look you up and rip you off. So, a little bit of anonymity affords some protection from thieves, who generally are thieves because they are lazy, too lazy to figure out the person is behind that screen name.
Then too, at the beginning, folks may have thought that there was a freedom of expression aspect; free to say what you think as opposed to being guarded.
That is, I might not say what I really think and pull my punches, but for that screen name.
Of course, there really is no anonymity for the average poster of anything anywhere on the internet. Yeah, the criminals achieve it but they have to work at it.