It's because it happened gradually / naturally / semi un intentionally, because:
1) SSN was not intended as a national ID, but it so happened to fit the shape of one, in that almost everyone has one and they're unique.
2) It has never been possible to institute an intentional national ID system in the US for political reasons
That is the recipe for the problem we have now. Strong demand for a national ID from many business purposes, the existence of something that looks a lot like, but is an imperfect form of, national ID, and the refusal to create a proper national ID, has naturally led to a de facto system of abusing the SSN as a national ID and just kind of everyone being a little annoyed and sketched out about it but putting up with it anyway for lack of alternatives.
Incidentally, did you know anyone can generate a valid new EIN (which is a lot like an SSN, and can be used where an SSN can be used for some but not all purposes, specifically filing taxes and ) at this page https://www.irs.gov/businesses/small-businesses-self-employe... ? This isn't legal advice and I'm not a lawyer and I don't know in what situations you personally would be legally permitted to use this (it's meant for businesses, absolutely not some kind of personal alias) -- but technologically, it's just honor system, and anyone can certify they need and are entitled to a new EIN and the IRS web site will provide you with a new unique one. I don't think you even need a legal entity, since you don't need a legal entity to run a business in the US.