The world would be a terrible place then

What you basically suggest comes down to everyone telling the world everything they know, i.e. a society in which there are no secrets. I don't think that such a society is possible in the first place but even if we assumed that it were, it would quickly disintegrate and atomize because it will be impossible to make a simple social contact between two persons. People would know what other people are actually thinking about them by openly declaring their thoughts and attitudes, and that would wreak havoc in social relationships. In other words, some things are better left unsaid, and this is where anonymity, or rather the need for it, kicks in