No. I'm not sure what the circumstances would be where I would have to present an actual social security card. Certainly never encountered one. Whereas it's easy to imagine circumstances where not having a driver's license on me could cause issues--even if it might technically not be required.

I used to use mine (plus my driver’s license) as my I-9 employment verification documents. Driver’s license for identity, SSN card for right to work.

You can also use a birth certificate to establish right to work, so yeah it wouldn’t be required.

Of course now I just use my passport, but like many Americans I didn’t have one for many years.

Fair enough. Not sure why I even carried my SSN card at that point. I've had a passport since I was around two years old.

You don’t need it because it’s so weak that people will accept that knowing the number is the same as having it.