But if you don't sign your bank card, and someone else steals it- then THEY can sign your card for you. And they can use it as ID. There's no reason not to sign it because of chip and pin, they need your PIN number to do any transactions in person, and if they do a transaction by phone or online, they have all they need on the card anyway!
Besides which, if you read the terms and conditions, your card is actually invalid if you don't sign it, and technically you could not be refunded for fraud on it if you hadn't signed it.
Beth