No, they aren't giving up booking. They are extending booking to a third party. To solve the problem with race conditions (You book the last seat on the airline, I book the last hotel room, and neither one of us can finish the transaction) you have to centralize all the booking in one party, which no one will do because they want to be able to upsell you at checkout.
Airlines, hotels, etc give up booking all the time to third parties. That's what booking.com is.