Le roi est mort, vive le roi
Assume we get rid of Socialist Security Numbers. It won't make any useful difference because the entities that wish to track and trace us want us to have a unique Identifier of some kind. Everyone was assigned an SSN by a government entity and could not change it. No better human-tagging system existed so it became the default US ID Number. But times have moved on.
If we stop using the SSN for identification some other Primary Key will be chosen to tag us with. The easiest new identifier choice would be an existing one that has lots of data attached to it already. What fits the bill best? Your Google or Facebook ID. The one they're sharing with the Feds already.
So my informed-cynicism take is that we can kill SSN for ID but it will be quickly replaced with something worse, probably your electronic ID from Google. I hope I'm wrong, but...