You don’t necessarily need to present your Social Security card as far as I know - I linked to what I think are the requirements below. I used my birth certificate and driver’s license at my current job, for example. https://www.uscis.gov/i-9-central/form-i-9-acceptable-documents
I mean, when every place specifically asks for your social and ID, yeah you do necessarily need to present it.
I ain’t carrying my birth certificate around with me.
You shouldn’t be carrying your social security card around with you either.
Maybe it’s regional? They don’t ask for my card in Michigan. But I do need to present it for a few things done at the SOS office. That’s the DMV in Michigan.