The State department isn’t collecting it for random reasons or for use as an identifier. It collects it for diplomatic purposes. So it is limited for a specific purpose.
I agree that SSN shouldn’t be collected inappropriately, but for purposes where it’s necessary, complaining that “the government” doesn’t need it, is silly, I think.
The more places your SSN is stored, the higher the likelihood of that information being misused by those with "legitimate" access, or stolen by malicious actors.
The same thing applies to pretty much anything about you (name, DOB, address, etc.), which should be sufficient reason alone to not want it spread around more than absolutely necessary.