The fact that it's fixed / can never be changed is a massive problem with social security numbers. That, and the fact it's often used as authentication instead of identification. They're moving away from that slowly, but it's taking a lot of time and effort.
The problem with ssn is specific to the US. Other countries have sane ways of authenticating citizens and the personal id number is just used as a global foreign kes for all government or public or bank database where you need to uniquely identify a citizen.
