You need to look at ticket prices inclusive of fees, not just fares. Those have continued the long run trend of falling in inflation-adjusted terms, although not every year.
Airline products across carriers have become less variable/more standardized. Price is only one element of competition. There are significant barriers to entry in the airline industry, not least of which is the prohibition on foreign ownership of US airlines. However that is hardly the only one.
The major reason Alaska Airlines purchased Virgin America was access to gates and in some cases slots at major congested airports. You not only have government-owned airports entering long-term leases with incumbent airlines, you frequently have capture of the bureaucrats running those airports by their major incumbent airline tenants. And where you have multiple airports in a metropolitan area, they’re frequently jointly run by the same bureaucracy rather than competing.
Airlines are highly profitable, though not nearly as profitable as two years ago, the biggest delta has been fuel cost tied to the price of oil. Consolidation allowed airlines to capture much of the gains of lower fuel prices for a period of time, but the smaller number of carriers returned to expansion and competition on the basis of price competing away some of those savings-driven prices.
All that said the only monopoly air routes in the US are the ones no one wants to fly and that require government subsidies in order to entice carriers into the market. Which isn’t to say that consumers wouldn’t benefit from more competition than we have today.
That is from Air Genius Gary Leff.