Why do social security cards exist? I have no idea, but presumably they are required for something. They don’t contain your photo, so asking for photo identification seems like a totally valid follow up.
Because they were invented to not be an ID, even though they got turned into one almost immediately (because of course they did). Then people dug in their heels about making a better national ID because reasons. So we’ve trudged along with a terrible one instead.
Even if your SSN is not an ID, there must be a use for the card/number is my point. If there is a use for the SSN, then you still need an ID to verify that you are the person to whom the SSN belongs to. So you still need the name on the SSN card to match the name on your ID. So you need to keep your SSN in sync with your other IDs.