The post office wouldn't take my credit card because it wasn't signed even though I showed them my driver's license. But they would take a debit card signed or not, and no ID. I just smiled at the lady and didn't give her any grief, but she apologized to me for the rule.
If I sign the back of the card credit and I lose it then the thief has only to practice enough to get their scribble to look something like mine. If I don't have it on there then they have no idea what my signature is and it would be relatively easy to say, "Hey look, that's nothing like my signature," when I disputed the charge.
There are times when the cashier never even looks at me, just the ID and the credit card. I've even signed "Mickey Mouse" on receipts and they have taken that.
But it matters not, since I've seen that even bank tellers don't verify closely. I had written a check to someone and later got the cancelled check back with thick black marker written over the payee name. The bank cashed it, and then had the nerve to charge me the "research" fee to figure out what happened concerning their mistake. Yes, I got my money back but to try to pawn that off on me was pretty annoying.