I agree that government proof-of-identity systems are actually pretty decent, and I think they could offer something really useful by making those services available as cryptographic proofs. In America, using a government-issued proof of identity over the internet amounts to sending someone my SSN, or a picture of my passport or drivers license. Obviously this sucks because they can now convincingly impersonate me on the internet.

If they also provided some kind of public-key database, any internet service could verify my identity without learning how to impersonate me. If I lose my private key (or it gets leaked), I can go to the DMV or whatever and have them revoke my old one and issue a new one, just like if I lose my physical license today.

EDIT: I know, Estonia/Iceland/whoever already do this. Not an original idea.