That is a great question! The challenge (as I see it) is that SSN is used across multiple companies and government orgs. If you give a bank, then an employer, and other unique IDs, how would it tie to the IRS for taxes, if the IRS has a different unique ID (or Social Security, as a functional example)?
I'm all for a different way, but the unfortunate intertwined nature of identification (in its current form) is a challenge... and pretty messed up IMO.