Sure, but a public key could still be stored in the case of a security audit. And I don’t think the majority of mass breaching are on the paper level. We need a solution to allow a new revision of an identity to be issued, possible something block chain like.
Why does the block chain have to be applied to every problem? We already have a solution for this, many businesses and the US military use it - smart cards.
Generate a private key on the card, have the government sign it, keep it locked up with a PIN/password (and self destruct after X number of invalid attempts). You can verify authenticity offline as long as you can request the card to sign a response and verify the signature, problem solved.