Are social security numbers useless by themselves?
Please remember that SSN numbers are NOT random. They include data like where it was issued, and what year it was issued. This might not be hard data, but it can be used to infer data about the person it was issued to.
The number is divided into three parts: the first three digits, known as the area number because they were formerly assigned by geographical region; the middle two digits, known as the group number; and the final four digits, known as the serial number.
While the number in complete isolation is not useful, you can leverage it with other info.
Not to mention that it is used for identification for other means (like employers, health insurance, banks, etc.)