In some cases it would be a lot easier and/or better if it was possible to identify and not just authenticate an user. This could include such things as turning on real name for identified users, or limiting elevated rights to them, thereby avoiding renomination of banned users.
In a lot of countries it is now possible to get access to systems with highly trustworthy identification. This is at least possible in several European countries, and I bet it will be quite common in the coming years.
If some users are identified and some not, what would be the pros and cons? I guess the difference should be visible somehow, but would it be necessary to show who is identified everywhere? It could perhaps be interesting to show the persons real names, but that would not be necessary? I can't see that identification at the system should imply public disclosure of the same information.
Some pros; - reclaiming user accounts would be somewhat easier - real names could be used (no impersonation) - user verification of various public departments - proofs of identity for copyright claims
Some cons; - non-identified users might feel they are second rate citizens - easier to stalk users with real names ((trans)gender problem?)