Maybe it isn't legal? I'm pretty sure there is a law preventing use of social security numbers for some things, so there may be something similar happening here. I don't really know, and I'd also guess something like that would vary by state.
A true solution would have to be usable by private industry as well. If it were up to me, it would essentially be x509 (because today, you're trusting the state and the person presenting the SSN), but people lose important shit, even proof of identity, all the time.
I never understood the privacy concern that americans have about a national ID card when the government knows all the same things about them, and can abuse it in all the same ways. It's like having all the downsides of a national ID, without the upside of being protected against identity theft.
And as to why the SSN is the way it is, it's a usage of convenience. Before the SSN there was no unique identifier for every citizen then suddenly to keep track of the new entitlement and assistance programs during the great depression one was created and companies started using it as they wanted because it was the most convenient uuid available. There's a good recent CGP Grey video about the history of SSN and why it's such a silly mess today.
Keeping us afraid is good business for a lot of low-rent grift industries, like doomsday preppers, as well as high-level ones, like the military industrial complex.
Obviously that Id can't be kept secret.
In Ukraine we even have an opt out for crazy Russian churchgoers who believe, that having id is literally selling their soul - they just use passport number in their x509 certs.
We must have something like unique individual IDs, but a significant faction of political actors don't want it, so nothing official exists. Instead we get terrible, insecure, miserable-to-deal-with, ad hoc, de facto national IDs of various kinds. It's the worst of both worlds—no actual extra freedom, lots of pointless inconvenience, expense, risk, and anxiety. If that last list looks like what our health care system produces, too, that's not an accident—this is the kind of situation our government (and their private partners) excel at creating.
It isn't now. But it used to be meant that way. I'm not sure what or how it started.
But old SSN cards had a line printed on them (on back, IIRC - probably not the best place) which read something like "For Social Security (or maybe IRS?) Use Only - Do Not Divulge".
That line has quietly disappeared (sometime before I was born - my Dad and my Mom's SSN cards had the line, but mine doesn't). Likely because the cat got outta the bag, and they realized it no longer mattered.
I imagine that it probably started with some company or other government agency deciding to use it without authorization of the SSN/IRS - and people went along with it because "it's the government, we can trust them", or some such malarky. Furthermore, most people probably never read the back of their card to find out that they weren't supposed to give that number out to just anyone, and of course no one thought of the potential implications to which that number could be applied.
This of course applies to any form of ID using a unique identifier: Bad actors in the system can easily exploit it - and when you are identified by a number, that number (and everything attached to it) is you - regardless of whether it really is or isn't.
Of course - all of this and more was covered in the book "Database Nation" - which was widely ignored.
https://en.wikipedia.org/wiki/Identity_documents_in_the_Unit...
For the best education on this insanity that I can reference:
Social Security Cards Explained - CGP Grey
For driver's license numbers, I've been asked in multiple situations to show it (for banking and employment), and seen the number written down.
It's still a slightly odd relic because I certainly would never want to depend on my SSN being secret. Even when used properly, that's still pretty wide usage.
Obviously SSN is treated as secret when it isn't. I've heard noises about re-issuing SSNs from deceased people, but didn't think it had happened. But is it not unique among living citizens? That's huge and I've never heard of it.