Doesn't 2-factor solve this problem? How would registering for SSN + 2FA be any different than registering for a SSN? Turn the SSN into a (not secret) usernam

Doesn't 2-factor solve this problem? How would registering for SSN + 2FA be any different than registering for a SSN? Turn the SSN into a (not secret) username/uid and add a 2-factor seed that's a shared secret between the SSA and the individual. Provide an API for 3rd parties to validate (SSN, 2FA code) pairs. If things go wrong, 2FA seeds are lost, etc, there's the same fallback that exists for lost SSN cards or stolen SSNs: go to a SSA office and get it fixed in person. The SSA could provide an online SSL-protected client-side webapp to generate 2-factor codes for those who don't have a smartphone. They could offer it as a telephone service too.