That's essentially how they worked before instant electronic funds verification. Old timers like me remember when retailers would pull out a large metal slab with a cut out area for the card. They would put a piece of paper over it with blue carbon paper between two sheets and pull a slide from one side to the other, making an imprint of the numbers onto the piece of paper for the customer to sign. One copy would go to the customer, the other would be kept with the retailer.
For a while after electronic transactions companies would lug them out when the "lines were down," but I haven't seen one in quite a while.
Here is a "modern," light weight plastic version:
https://banksupplies.com/199-48500?origin=google-shopping&gc...