They can charge the credit card without us having to type the pin code (e.g. when making online bookings with prepayment), so why won't they do that at checkout?
It's very easy (and unfortunately quite common) for card holders to create chargebacks for retail purchases they legitimately made on their credit card. At hotels, it's even more common to come across unscrupulous travellers seeking a cheap vacation who rack up a bill worth thousands of dollars and charge it to a fraudulent credit card along with stolen or fake identification. Weeks or months after checkout, the hotel will see the entire amount reversed by the bank, and they have very little recourse to recover those funds. The chip-and-pin system is designed to completely eliminate the possibility of fraud. Banks are so confident in this technology that if fraud does occur using the chip-and-pin system, the bank will accept full liability and the hotel will not lose a dime. Even if a credit card number and CVV was provided during the reservation and a deposit was applied to the card, it would be irresponsible for the hotel not to verify that card by requesting the balance be pre-authorized using chip-and-pin (on the same credit card) upon arrival, thus proving to the bank that the card holder has indeed authorized the transaction.
The PIN is required to do a chip & pin transaction. (The credit card itself is a Smart Card if it has those metal contacts in the side. They are to connect to the card's "chip". Much like a SIM card for GSM phones.)
The PIN is used to unlock the card, so it can authorize a transaction. This is checked by the card itself, and getting it wrong enough times in a row (usually 3) will lock the card.
As a result, the risk that someone's using a cloned or stolen card is greatly reduced. (Since only the card's owner should know its PIN code.)
I expect most payment processors require the use of chip & pin wherever it's available, or at the very least give lower fees to merchants when it's used.