Because it's not wise to allow anyone to have unsupervised access to your card like a cashier/ server /waiter/waitress. They take your card to run the transaction and just might jot down the card info to use later for an unauthorized charge before bringing it back to the table for you.

Back in the early days they used to run your card over with a roller on a form in a machine containing carbon papers to transfer the card numbers to the charge sheet. They also called a number to see if the card was any good.

I always asked them for the carbon papers after I signed those slips. Many a time they would get indignant saying they were thrown away.

My reply was always, first off carbon papers floating around in the trash can is hardly a secure way to handle them and secondly you did not trust my word when you called to see if my card was any good so why should I trust you to securely destroy the carbon papers with my card number on them. 

I often got an apology and admission that they had not thought of it that way before and I ALWAYS got the carbon papers with the receipt.