When you sign the back of your card, you're providing a template for forgery to anyone that happens to steal or find your card. I can understand why the credit card company would want you to do this, as a convincing forgery job on a signed sales receipt shifts liability from them to the consumer. However, as a consumer, I don't understand why you'd willingly buy in to such a system.
Because signing a credit card isn't for verification. It's for agreement of the terms and conditions.
Signing the back of your card is how you indicate that you agree with the terms of your cardholder agreement, which your provider has spelled out how you pay them back, how they charge interest, what interest rate, billing, etc. If you don't sign the card and the merchant accepts it, then they have to eat the loss because you didn't agree to the terms.
Likewise, signing the chit just means you agree to pay the amount shown in line with your agreement.
It's just contracts, in the end. The card signature shows you agree to the contract between you and the credit card provider. The chit signature shows you agree to the contract to pay the amount shown. If someone else forges your signature, that's fraud and you're not responsible. Likewise, if someone uses your credit card with their signature, that too is valid since it was signed under agreement.
There's nothing special about the signature. Banks routinely loan out lots of money without even a "reference signature" to compare to, yet they're still valid.
You're just signing to show you agreed to the presented terms.
If you look closely, the chits all say "Cardholder agrees to pay the amount shown per the terms of the cardholder agreement" which is what you're REALLY agreeing to.