I was in a similar situation, and then I found out I'll need to show it AND my birth certificate to renew my drivers license. Words cannot express my contempt for this BS.
I've been working for 40 years, and I have yet to see my SS card.
Anyway, I finally found my SS card, and, bought a new copy of my BC. (The laughable part is that anyone can buy a copy of the BC and claim to be me! So exactly WHAT does possession of the BC prove? Nothing!)
The kicker is that when I looked at my SS card, it was emblazoned with a notice that it is NOT to be used for identification purposes!
The more I observe of the madness surrounding modern "society", the more I am reminded of Poe's "Descent into The Maelstrom."
You're lucky. In Texas, I had to show the social security card, birth cirtificate and marriage license. They explained to me that it was a requirement of The Patriot Act. (Actually, I substituted an out-of-state DL for the SS card.)