It's a remnant from when physical card theft was the main concern: You're supposed to sign the back of the card when you first get it, then each time the receipt is signed the cashier is supposed to compare the signature on the receipt to the one on the card.
I remember as a teen reading some stories about how cashiers wouldn't accept cards that didn't have a signature on the back and made people sign it right there in the store, apparently not at all understanding the purpose of it.
That’s what’s supposed to happen, but in my 20 years of using a credit card I can only recall having my signature checked like this one time. I assumed the person was new. She ended up getting the manager and I had to show multiple forms of ID to prove I was me. It was a whole thing.
Now that we sign electronic pads, it’s even worse. There is no record of the signature on the back of the card to compare to, no one looks at it, and most of the pads are sensitive enough to sign properly. It’s a really expensive rubber stamp.
Now that I think about, I wonder if this signature business is a result of our restaurant norms. Since the waiter takes the card, runs it, and then brings back a bill to sign. If they switch to a PIN, every restaurant would be forced to upgrade to handheld devices, or have the customer pay up front on the way out. A worthwhile change imo, but I can see lobbyists fighting to avoid it.