Well then, how about charging more for faster flights, to account for fuel? I mean, domestic business class isn't that great, but people who pay others people money for it would presumably go for a faster flight.
The majority of people who fly do so in cattle class, where basically the headline ticket price is the biggest factor in choosing prices (which is why low-cost airlines offer cheap tickets but charge steep prices for doing things like bringing luggage or getting a drink on board the plane).
You can't fit enough people in first or business class to fill a plane on most routes, and you simply can't go fast enough to make speed premiums really worth it. Note that going to an airport usually requires on the order of 2 hours of hassle before accounting for flight time, which means that you've already lost a day of work in practice. No, unless it's a long-haul flight, there's little benefit to faster speeds, and the Concorde was never really profitable.
They did with limited success. https://en.wikipedia.org/wiki/Concorde