If the US government created its own SSO system and mandated that all government website used it as primary while allowing third parties to use it too this could become a solved problem. It would be a credential that could be accessed via existing paper based systems. Places like Google allowing it as a sign in method would actually solve this case. Sadly I think the tech world in general is so allergic to losing privacy that even something optional like this would get lobbied out of existence just by tech companies alone.