Yes. The whole idea is very flawed. It would be good if we got rid of it entirely but most people can't mentally/emotionally/financially handle that so we end up with a lot of bad compromises.

"Under a few rare circumstances, SSA may legitimately issue a new SSN to a person with a prior SSN. The conditions are highly restrictive."

https://www.ssa.gov/policy/docs/ssb/v69n2/v69n2p55.html

> From what I can gather they're supposed to be unique and they don't reuse them. If two people have the same number then it's a mistake.

Yes, it is a mistake for two people to be issued the same number and it is unusual for multiple to be issued to the same person.

However given the very large volume and the conditions under which things have happened (not just currently but back to 1936!) both mistakes and unusual conditions exist in numbers that cannot be ignored.