The whole industry relies on a certain symbiosis between the full fare coach and first class demographic versus the discounted fares demographic.
The few folks in the former group pay a hefty and very outsized fraction of the total revenue on the flight. While the many folks on various discounted fares are numerous, but their total contribution to revenue, much less profit is rather modest. At the limit, the cheapest of the cheapos in back are sold for just a dollar above breakeven marginal costs, given that flight 123 is already going from ABC to DEF on Tuesday.
And that given is the keystone of the whole system. In a capital intensive biz selling a perishable product, utilization is the key to profit. Keep the jets full and keep them moving.
Summarizing / simplifying mightily, an industry that had only first class or even first class and full fare (but only full fare) coach would be a lot smaller. There is demand for that product, but not ginormous demand. As a result there would be far fewer airplanes flying and far fewer flights per day between ABC and DEF. Which would inconvenience the fatcats and business travelers who want convenience and frequency and would be willing to pay something towards that.
Which Bizarro world was exactly what the USA (and most other nations) had in the old regulated era. What was discovered promptly post-deregulation in the USA in 1978 is that there is a huge demand for cheap travel. The challenge is how to provide it profitably. Bigger airplanes with cheaper smaller seats is one way. Hub and spoke operations in another way. Red-eye flying is a third way.
By adding in cheap coach seats the airline takes in more total revenue per flight but ever less marginal revenue per seat. As long as they can do that profitably they can grow the fleet and offer more seats between ABC and DEF. Thereby helping the fatcats and full-fares who want that frequency.
There totally are airlines trying various fatcat-only services. Typically they founder on only being able to serve a few city pairs that have enough factcat travel density to make it work. And they’re typically flying smaller jets like RJs, but reconfigured with many fewer much larger seats, better amenities, separate terminals to avoid the crowds, etc. IOW: trying to offer the private jet experience lite without quite the eye-watering pricetag of that truly luxo service.
There are also airlines offering no-frills cheapo only. Those typically hope to capture enough market share they can then quietly ramp the actual price while still loudly advertising that they’re still cheap. Southwest is now the world champion at that. Spirit is much farther back in its journey to transition from “is cheap” to “is widely believed to be cheap”.
As a separate matter, it’s absurdly easy for a new airline to get financing and jets and workers on the cheap. So at first their costs truly can be lower so their break-even fares are lower. After a few years’ honeymoon though, the airplanes come off warrantee, the workers who’ve stayed want real wages, etc. So costs start rising. Some carriers make the higher costs + higher fares = still profitable transition successfully. Most don’t and shut down. Then a new company springs up in their place to live the same lifecycle again.
Bottom line being it’s hard to survive as a urly high end or purely bottom feeding operation. The two together form a balanced diet. Different markets and different stage lengths demand a different mix for max profitability. But get too far off the standard mix and profitability becomes elusive or, if you deviate far enough to one extreme or the other, impossible. Then you eventual bankruptcy is just a matter of time and investor patience.