In Belgium we receive a national ID chip card which can be used as a PIN-protected client certificate on websites, including all government sites. Identity theft is pretty much impossible unless someone physically steals your ID.
I never understood the privacy concern that americans have about a national ID card when the government knows all the same things about them, and can abuse it in all the same ways. It's like having all the downsides of a national ID, without the upside of being protected against identity theft.
My best attempt at explaining, although this particular issue isn't one I feel all that strongly about: It's not that we're against the practical idea of a national ID card, it's that we're against giving the federal government the authority that would be necessary to mandate such a thing. We're willing to live with the inefficiency to keep federalism intact.
There's an inbuilt distrust of the federal government built into the constitution itself and there's a constant drumbeat from the Republican side that the federal government is wasteful and out of touch with the needs of the individual states, often for practical purposes of devolving control of funding and policy to the state level where in general they have more control.
And as to why the SSN is the way it is, it's a usage of convenience. Before the SSN there was no unique identifier for every citizen then suddenly to keep track of the new entitlement and assistance programs during the great depression one was created and companies started using it as they wanted because it was the most convenient uuid available. There's a good recent CGP Grey video about the history of SSN and why it's such a silly mess today.
The answer is, Americans are often fearful people about irrational things. (I am one, and I get into arguments all the time with friends about their irrational fears of the gubmint, terriss, communiss, you name it.)
Keeping us afraid is good business for a lot of low-rent grift industries, like doomsday preppers, as well as high-level ones, like the military industrial complex.
I never understood the privacy concern that americans have about a national ID card when the government knows all the same things about them, and can abuse it in all the same ways. It's like having all the downsides of a national ID, without the upside of being protected against identity theft.