In the UK at least you should never have to hand it over. You insert them into the chip and pin device yourself. A lot of places will do this for you but only in plain sight.

Well, in the US it is common to hand your card to servers after your meal who will then carry it off to the register (wherever that may be, usually not visible) and bring it back to you with a receipt.

The UK may have a better protocol, but that doesn't change the fact that for a significant population, the number on the card is really anything but private. Certainly Apple should know this, being based in the US...

This is usually ok since credit card companies have the whole fraud thing figured out for the most part. It only becomes "not ok" when companies like Apple make them into something that absolutely needs to be secret.