The summary is that the USA does not have an official national person identity number. The SSN is the closest approximation, so it is being (ab)used as one. This is despite that it is explicitly not designed for it and has some qualities which make it less suitable (the numbers are small and very predictable).
In general, nearly every national-identity-system suffers from a contradiction between assigning identities and identifying. Where the number you get assigned is simultaneously your identity and a secret you use to establish your identity. There are initiatives to solve this using cryptography, but this is complicated by political attitudes towards privacy and government tracking. I dare say in the USA this is more pronounced due to both the problem and the political attitude against solutions being more pronounced.
The summary is that the USA does not have an official national person identity number. The SSN is the closest approximation, so it is being (ab)used as one. This is despite that it is explicitly not designed for it and has some qualities which make it less suitable (the numbers are small and very predictable).
In general, nearly every national-identity-system suffers from a contradiction between assigning identities and identifying. Where the number you get assigned is simultaneously your identity and a secret you use to establish your identity. There are initiatives to solve this using cryptography, but this is complicated by political attitudes towards privacy and government tracking. I dare say in the USA this is more pronounced due to both the problem and the political attitude against solutions being more pronounced.