Let's call it what it is. The "Social Security Number" has lost nearly all association with "security".
It's is used as a national ID, it functions as a national ID and for all practical purposes it *is* a national ID number. If someone has your SSN, they can own your assets and there's nothing you can do to change or stop it.
I don't agree with it, I dislike it intensely, but fretting over the possible implementation of a National ID number is worrying about spilt milk. We have it. It's here. We need to fix it.