Each leg of the flight costs money. Forget that they are all happening in quick succession and let’s pretend they are all a day or week apart. What should cost more a flight from Miami directly to LA or a flight from Miami to Houston + a flight from Houston to Denver + a flight from Denver to LA.
Tldr 3 flights more expensive than 1 flight.
It is cheaper for them to fly you direct than through connections, everything else being equal(especially how full the flights are).
Airline pricing is ridiculously complicated, and adversarial with both the customers and the other airlines. They try to set prices wherever they think they’ll make the most profit, and showing a more expensive option that’s worse may make you feel better about the value of that $300 flight, even though they’re making a healthy profit on it. They’re still willing to sell you a ticket for a less direct route, but they’re not going to give up making a profit off you.
It also might be that the 3 layover option is from an airline that doesn’t have a direct route.
The airplanes use more fuel for longer flights then shorter flights. For each connection there is airport fees, landing fees and added fuel and maintenance for the airplane. So it costs the airliner more to sell you a longer connecting flight then a shorter direct flight.
The reason you even see the connecting flight is because airliners might have extra seats on the flights they do anyway and often decides to sell tickets at cost or even cutting all the fixed costs associated with the flight. So you end up just paying for the fuel and airport fee. The airline will not make much on this ticket but it will be better then not selling you a ticket at all and let a competing airliner sell you a direct ticket.
Often when there’s multiple weird connections they’re looking at multiple one way itineraries vs to get to your destination.
Will it work? Yes! Is it optimal/rational? Nope
The other flight options should feel like they’re crazy timings and/or too expensive. They’re anchoring your price/expectations so the direct flight automatically feels more rational. But are there other airlines, other dates, or other routes they don’t want you to think about??
To them, hopefully you won’t ask any of those questions
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