One more thing: they are sharing my personal data without my consent - in this regard, it is very different than me providing my card data over the phone.
They do have to share your personal data to the fulfilling agent just like you have to share your personal data to book a flight. The hotel has to have your information to complete the reservation and I'm sure it's buried somewhere in the terms and conditions.
Hotels will still ask you for your credit card, most (if not all) payments on Booking.com reservations are done upon arrival, and not online. So, honestly, Booking asking for your card details is completely useless.
Hotels might as well shoot you an email or call you to confirm - in fact, I think that would make for a better experience.