The reason the US lacks a national ID system ties back to a strongly held belief about state's rights, and that a national ID system would violate those rights, IIRC. I think it's already somewhat happened though, as I understand REAL ID to more or less be that.
Yup, I heard the same. SSN's are the relatively recent "compromise" made in the 40's. Initially as a way to access your, well, social security. In post depression times where people wanted security more than freedom.
ofc it was never meant to act as a national ID (and thus never tried to be secure), but more and more things are hacked in to make it act as such since there's no better option. A bit ironic given the state of social security nowadays.