Social Security numbers are unique. They don't work as a great identifier because they can be mistyped, can be hard to verify, and people don't want to give them out too much.

SSNs should be unique, the only exceptions are fraud or errors.

According to the Social Security Administration:

> At its inception, the SSN's only purpose was to uniquely identify U.S. workers, enabling employers to submit accurate reports of covered earnings for use in administering benefits under the new Social Security program. That is still the primary purpose for the SSN.