The extinction of air travel?

Because it is. When every passenger ends up paying a different price, its not good for anyone but the people who paid much less than the cost of service.

The other end of the complexity is the list of different charges that they use to cover up the fact that you’re paying higher than the “ticket price”. Fuel surcharges, gate fees, other fees, this tax, that tax. It’s like buying a freaking car. Just give me a basic price that covers all that, please!

Can you imaging walking into McDonalds to buy a Hamburger and they tell you that it’s $1.99, but then you have a $0.35 Grill Fee, plus a $0.25 Franchise Fee, plus a $0.15 Parking Lot Surcharge plus a $0.25 State Burger Tax plus, plus, plus… I dunno about you, but either lose interest and walk away, or be yelling at them to Just give me the damned price!

Problem for who?

The reason for the complex pricing system is to maximize profits, not squander them. Why do you believe otherwise?

Given the frequency of air carrier bankruptcies, it would appear to be less than successful.

That’s the reason, but it has had unintended side effects. All things being equal, it costs nothing to put a person in an empty seat (especially these days.) But businesses got good at gaming the system. Not all business trips are done at the last minute. The last bunch I’ve done, through my company’s contracted travel agent, have been about as cheap as the flights I got for personal use. Back when a Saturday night stay was required, we’d get paid for it, since it saved so much money. So the airlines and customers are playing chicken.
Pre-web it worked a bit better, since some travel agents weren’t going to work hard to get a flight on which they got a trivial commission. With the web, fliers have all the info the travel agents used to have, ans so can search for the the leftover seats.