I didn't mean to ignore this, I just wasn't following the thread, and perhaps you won't see this reply.
I'm not maintaining that the current status quo is optimal, just that it's more complex than what people traditionally think of as price fixing, which e.g. would be all the gas stations in your area deciding to charge you the same for gas via explicit collusion.
Speaking more generally, the travel industry as a whole has always and probably always will spend a relatively large amount of advertising of some sort. Most of the industry is hoping to lure travelers with no local knowledge to their properties or services, and they're competing with other local properties.
Before OTAs hotels might expect to pay this advertising fee to travel agencies, or to pay to be part of a hotel chain as a guaranteed source of customers.
The unstated desire of people opposed to rate parity is to somehow have their cake and eat it too.
After all, if almost nobody looked at these OTA websites why care about it? It's not going to have much of a financial impact.
But they do care, because OTA's are a major source of revenue. And why is that? Because people get a lot of value from those sorts of market intermediaries, not just in the accommodation business, but in the form of major chain stores, Amazon, eBay etc. It's easier to compare products when you have a standardized comparison run by an intermediary.
As far as I can tell the scenario hotels hoping for the end of rate parity want is one where consumers might browse OTA websites, but be savvy enough to just visit the hotel's website directly to make a booking.
I don't see how that's going to be sustainable, you'd essentially have advertising with a free rider problem. Ending it wouldn't be the end of the world, but I don't see how we wouldn't just end up in some new equilibrium where accommodations wouldn't just pay a similar amount of money for advertising via some other means.
It's not like browsing organic Google results for hotels is some arcane wizardry, or visiting a town's listing of hotels (which the hotels generally don't pay for or get at really good rates) isn't known to people.