In fact they did, called roomkey.com Hilton/ihg/marriott/hyatt/choice/wyndham options could all be searched simultaneously, and you get the lowest price and the hotels avoid paying commission to Expedia and booking.
But they shut it down. I wonder if it was because hotels are usually franchised, and the brands get a percentage of revenue as royalty, so they don’t care about commissions the hotel operators have to pay. So they decide to price discriminate via the travel agents.
It should be similarly trivial for the airlines and car rental companies to get together and offer the same website. Isn’t it better to give customers a 7% discount rather than give booking/Expedia 15%?
Obviously, reality is different so there must be a reason. I’m guessing the gains from price discrimination are more than the losses from commissions.
Plus it is hard to get competitors to work together on something. Orbitz was started by a partnership of airlines. It IPO'd and then was acquired by a private company, all within 3 years after launching. https://en.m.wikipedia.org/wiki/Orbitz
If it isn't obvious yet, the enormous reach and scale of the internet does the exact opposite, it basically guarantees consolidation. Booking and Expedia each used to be 4 or 5 independent companies. The booking engines wield power by de-listing any operators who offer lower prices anywhere else, and none of the hotel chains can risk not appearing on the sites, even more so when there are only two.