America historically was not very federalized, and being able to just abandon your life and move out west is a key part of the country's mythology, if not the DNA of the country. So there have always been attempts to resist a national ID system, and the SSN was originally not supposed to be used for this purpose.

Of course in 2019 this is basically a moot point if you want to be integrated into society, but even then there are people who are legitimately not integrated into the modern US economy by choice.