How is it terrible? SSNs rather reliably identify individual people, actual non-fraudulent collisions are very rare.
The fraud is a separate issue and SSNs are obviously misused, but that doesn’t mean that it’s not a reasonable system to uniquely identify multiple people with the same name and DOB.
The fact it is tied to social security and is not called “national ID” shows already it is a legacy system, + the fact there is no authentication in place
Authentication is completely separate from identification, you shouldn’t be using any kind of ID number to authenticate anyone. That does not suggest that ID numbers are not good for identification.
The fraud is a separate issue and SSNs are obviously misused, but that doesn’t mean that it’s not a reasonable system to uniquely identify multiple people with the same name and DOB.