> It no longer says this, and has not for a long long time.
Don't know about "a long long time" but the feds have been treating Social Security Cards as identification since 1943 (military, some agencies) or 1963 (IRS) (cf [0])
I think you're misunderstanding why they are requesting an SSN. You cannot use an SSN to do an in person ID like a photo ID. Same reason a birth certificate cannot be used as an ID. These documents can be used to look up information about you, and a lot of places might use your SSN as a database unique ID, but that kind of info is not identification when someone shouts "papers!" at you.
conflating the two meanings of identification feels deliberate at this point
