Maybe it's time the government develops a system for one time use keys for social security numbers. So, when companies want to do credit checks or background checks. It's only good for that one check and they don't get a persons real SSN permanently.
Perhaps for the purposes of credit. People can generate two keys. One being a one time use for a credit check. The second only able to send updates. Such as credit limits, usage, missed payments, &c. But is not possible to use for any new credit checks, lines of credit, &c.
That way people won't have to reveal their SSN. This could also be applied to employers, 1099 wages and so forth. They don't need your SSN. An alphanumeric key only good for reporting wages and such is all they need. As it would be keyed to your SSN.
Basically a system which minimizes the number of sources with your actual SSN. While still allowing checks and reporting. With random keys which have a limited scope of usage.