The major airlines very much have brand loyalty via loyalty rewards programs, lounges, and cobranded credit cards.
If you are business traveler gaining status by flying a preferred airline and using other people’s money, you aren’t going to go to the cheapest airline.
Most of the profit from the Big three airlines come from business travel and credit cards
This! I'd argue that the only reason loyalty might not always matter is because I am frequently not given a real choice because a given route likely has a very limited number of airlines offering flights and those might be dramatically different in number of stops, price and times. Air travel is one area where I frequently wonder how many benefits of it being a free market on paper we are actually getting. There is limited choice and direct competition seems limited
One of my semi-frequent routes is between MCO (current home) and ABY - a small airport in Southwest GA where my parents live.
There are only two commercial flights a day, both on Delta and both to ATL. A round trip ticket is $540 for two 1 hour segments (MCO - ATL - ABY).
A round trip ticket from MCO (Orlando) to LAX (Los Angeles) is about the same price
Of course I know the trick for former - book through a partner AirFrance for 17K miles