Well, understand that eliminating Social Security Numbers does NOT necessarily eliminate the Social Security Administration. This agency is an independent agency, NOT under the U. S. President. It was created via U. S. Code.
To eliminate the agency would mean rescinding the U. S. Code that applies to it.
Creating crypto keys that would be issued by and under the Social Security Administration would be a BIG mistake, if those crypto keys are required to be used for identification everywhere. It would defeat the purpose.
Social Security Numbers should ONLY be used when interacting with Social Security Administration with regard to the services they provide. So, I think the agency should stay, should use crypto keys, and be voluntary.
For people who opt out of it, whatever organization they use for retirement and other benefits should also use crypto keys.