You're probably too young to remember, but back in the bad old days, we'd write stuff by hand. It didn't feel laborious because it was all we knew. We'd copy name, address, license number and expiration date, and eyeball that the person in front of us looked close enough to the picture.

You just write the relevant information on the carbon with a pen.

> we had an old carbon copier that we could use

You know, the kind where you slide the thing across and you don't have to plug it in?

That takes an impression from a credit card (although I see more and more that don't have raised lettering) but not from an ID.

The impression isn't strictly necessary -- it's for convenience and, if needed, solid proof the physical card was there. At most you write down the license number on the carbon paper. If you lose the machine you can hand-write the card number just as easily.

Think about how an online transaction works -- punch in the number, no ID needed. Believe it or not that didn't start online ;)

Source: took "offline" payments when a retail store's power went down many many years ago.