SSNs are identifiers and not intended to be private. The only reason anyone cares about SSNs is that some private businesses were negligent in their authentication procedures and have tried to shift the blame to the victims.

In contrast, if you have public-key encryption people are going to build systems on the assumption that your private key is only available to you despite several decades of history showing that's not a safe assumption.

Your SSN you can memorize. A 2048 bit+ private key is gonna be a lot harder