If they could push a button and use new identifiers, they'd do that today.
However, in reality that means cracking open 50 years of code and systems.
What else would you use though? (in the US)
I can't think of any broadly-existing alternatives. You could perhaps have people opt-in to a newly-created, cryptographically-secure ID replacement.
It ultimately falls to the government to provide a more robust solution.
In Europe, we use these as "root of trust" - either in physical form or in electronic form.
You aren't required to posses one in Europe either, but you get assigned a unique number at birth to identify you.
Of course life is hard without identification, but there is no law mandating that you get one, at least not in all EU countries maybe some of them do.
Financial institutions in America prioritize convenience over security.