> 3. Public identity, suitable for displaying to other users
Many sites-- like HN-- may not even need that. If you have system and login identity you can just display "dingus" as the name of every single user and the system should still work the same.
I think without display names having discussions would be difficult, as people find some identifier useful to follow along. Even if it's a pseudonym, it's hard to build a sense of community without being able to distinguish those in your community. Or am I misreading you?
It's a different kind of discussion, though. There is value to each type of threading, but no one-size-fits-all approach--as evidenced by the fact that 4chan lets you opt out of anonymity.
Many sites-- like HN-- may not even need that. If you have system and login identity you can just display "dingus" as the name of every single user and the system should still work the same.