You authenticate everywhere using a long number (PIN) (so long you have to write it down and store it). All the services you authenticate with will store this PIN unhashed.
You should keep your PIN safe, because it can be used to apply for bank accounts, loans, and commit tax fraud if it is stolen.
If you ever forget your PIN don't worry. We will print it on various letters and mail them to you. If you need it urgently, you will find it next to your name in various post-hack data dumps around the internet.
They started issuing cards with an EDIPI on them relatively recently, which is a step in the right direction, but there's still a lot of work to do.
The DOD originally switched to the SSN from the previous service numbers, as in "name rank and serial number". It was a convenience measure, since the service number system was arcane.
Service numbers were also public record, and I've read documents indicating that social security numbers were not considered sensitive information (notwithstanding the fact that the DOD didn't have the concept of PII formalized back then).
Should the DOD have moved back to another serial number system sooner? Possibly. I'm amazed that they're moving at all.
Things are getting better and the DoD has switched to a non-SSN identification number but the SSN is still frequently used.