As someone who has been in the industry a long time and knows it well : for most hotels booking passes the CC information direct to the property.

After the booking is over, the hotel pays a commission for all reservations directed from booking, usually around 15%. The third parties are essentially advertisers for the hotel and nothing more. In every aspect, the booking is the same as direct and hotels sign a contract agreeing not to undercut the third parties.

What happens is that hotels get mad about a percentage of revenue going to another company, so they blame everything on the third party when in reality they can literally press a button on an app and have a third party booking cancelled. On top of that, management doesn't give front desk any authority or knowledge of the wider systems until they become management, so third parties seem complicated and mysterious when really it is no more difficult than selling on ebay if you just engage with the technology and give admin rights to the workers.