I don’t agree that prices would rise, overall. I occasionally fly home to Glasgow, and have been doing so for 40 years. These days, I nearly always manage to get a decently discounted rate, and sometimes a heavily discounted rate. It works, making me feel I have got a bargain. But when I look back to the prices of 1980s when all were fixed, and then adjust for inflation using Bank of England calculator, the 1980s prices were broadly similar to today’s typical actual ticket price. Plus we got free booze and free food, a lot more legroom, no charge for luggage, and prettier air hostesses. Ok I admit, the last item might be my imagination, but I’m fairly sure about the rest.
Fixed prices might see the disappearance of the occasional spectacular bargain on a flight or hotel but every time a hotel or airline offers a spectacular bargain, they have to charge another customer more to make their books balance. If we could get away from advertising “prices from xyz”, and move to “price is xyz” then it would create more competition to drive down actual prices. Only my opinion, of course.