Yep, but the US never developed any alternative form of universal identification so people gravitated towards the SSN for that purpose, even though it was explicitly not to be used for that.

What other options are there? Most other potential identifiers are full of pitfalls like input error, collisions, having things change, or simply being unknown by the citizen. Even something as simple as name, birthdate, and place of birth is chock full of problems. People transcribe records wrong, or were born out of the country in a place with no recordkeeping that no longer exists to parents who have since died.

SSNs are far less complex and error prone. Their only major downside is that they only work for people who have them, which means your app can only service legal citizen Americans.