Yeah, good luck with that.
Good grief..
Obviously,the SSN in the United States is a pretty faulty method of identification - there is plenty of fraud and errors in it. Anytime you suggest some sort of secure and comprehensive identification method here - you catch a $hitstorm of criticism from those who are paranoid about privacy concerns.
OK, then do it like the “Safe Traveler” credentials program which are offered at some airports for frequent travelers willing to undergo a background and identity verification process - i.e., make it voluntary.
It won’t be comprehensive, because some will opt out. But they can chose to do that, and as long as government services are both required to use a high level of verification, and allowed to recognize and utilize the secure and advanced credentials system (with some attendant benefit in terms of speed or cost to the identified citizen), what’s the problem?