Yes, the only role of the government was to issue an SSN which has been explicitly said shouldn't be used in such a manner[1].

It is a real pet peeve of mine that people take such hard stands on issues like this when it's so easy to check what's actually happening first. This thread isn't the most egregious example, but it is an example of someone just imagining a system with a big flaw and then suggesting a solution to the problem they made up.

[1]: https://www.scientificamerican.com/article/social-security-n...