> There's nothing wrong in using SSNs as an identifier.
There's plenty wrong with this. SSNs were already a pretty bad identifier when they were invented and didn't get better.
There's no check digit, so if you make any mistake at all it's probably a different person's valid SSN.
Until relatively recently they were assigned both chronologically and geographically, so one digit error in SSN plus Address plus date of birth... Causes no red flags, it looks about right. Modern ones are randomly assigned, but it'll be decades before that's most people.
Like most similar systems the US SSN also very explicitly says it isn't suitable for any purpose except numbering Social Security recipients. People you want numbers for may or may not have SSNs. Don't worry though, since they all look pretty similar and there's no check digit the people who don't have one long learned to give a bogus SSN, probably belonging to somebody else. Somebody you know probably does this today. What a useful "identifier".