I agree that using a real identity forces people to be more deliberate. Also, idealistically, I agree that we should own our convictions.

Realistically, people's convictions change over time. The internet on the other hand is mostly undated. A Google search doesn't return a persons online activity in reverse chronological order. In a traditional environment the absurd things we might say as a result of past convictions will fade as time goes by. Consequently the perception people have of us is biased towards the present. This isn't true for the internet and anonymity is the only way to keep our identities from stagnating.