So if the SSN stops being considered as a combination identifier/authenticator, other government agencies stand eager and ready to plunge headlong into the same mistake.
The way around it is to pass a law that requires government agents and agencies to consider identifiers to be public, and authenticators to be secret, and that nothing can ever be both. The government could require itself to publish indexes of names to SSNs and SSNs to names, such that no stretch of anyone's imagination would ever generate a presumption that knowing the number proves you are the person to whom it is assigned.
The ridiculous assumptions made in the credit and credit reporting industry that are held out to be reasonable should never be allowed to hold up in court.