One problem with using an SSN as a identifier is that the number exists for the administration of the Social Security system, so only people who pay into or will receive money from the system are eligible for a number.
Not everyone in the US is eligible for an SSN (e.g., some non-residents living in the US). When I first came to the US as a student, I had difficulty doing things like signing up for a credit card or a cellphone for this reason.
There are other numbers that systems sometimes but do not consistently accept, for instance an ITIN, which is the tax ID number the IRS will issue you if you aren't eligible for a SSN.
Not everyone in the US is eligible for an SSN (e.g., some non-residents living in the US). When I first came to the US as a student, I had difficulty doing things like signing up for a credit card or a cellphone for this reason.
There are other numbers that systems sometimes but do not consistently accept, for instance an ITIN, which is the tax ID number the IRS will issue you if you aren't eligible for a SSN.