They say to get the card out of its safe hiding place in our home only on the day that we will need to take it to the doctor or other health care appointment. (Every time I hide something in a 'safe' place, I lose it. Still haven't found that copy of my birth certificate that I obtained a couple of years ago - finally just went and got another copy.)
I thought it was important to have the proof of health insurance with us at all times in case of accident. I don't know if a hospital would even provide treatment without it. Insurance plans differ as to coverage amounts and what kind of approvals are needed for various procedures. Maybe all this doesn't matter in an emergency situation.
I don't know - do you carry your card with you at all times?
I found a thing on the Internet: Rare Color Photographs from the 1930s and 1940s.

I think these were circus performers, which might explain their interesting clothes and hair.