Earlier quoted context omitted.
SSNs are problematic because they are expected to be both public and confidential. In reality, they're public. The federal government refuses to issue actual public IDs, which would solve the problem nicely, for political reasons. They can't retract Social Security.
That is one reason they're problematic, but not the problem I described. Public IDs would make the problem I am describing worse , as even more businesses would unashamedly ask for them. People's feeling of "oh isn't that private" is one of the few things holding back everyday retail businesses from asking for them.
have you considered adding a good PII protection laws to circumvent that? GDPR seems to work pretty well.