The best solution would be if the US introduced mandatory passports or other forms of ID cards with smartcard capability, similar to the German Personalausweis. It has a secure cryptoprocessor with key vault, meaning it can be used to sign documents (if the bureaucracy to get a signature CA wouldn't be completely stuck for years now, SIGH), but especially companies willing to use authenticated data can fetch them securely over any NFC enabled terminal. Quite ingenuous.
This would entirely kill ID fraud at the source. The problem only seems to be an aversion in some parts of the US population against ID documents.