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.