I'm a little iffy on this idea that there is any monopoly on air travel in the US in any general sense. Maybe for specific routes, but if you look at the big picture, you have:

4 "major" carriers - American, Delta, United, Southwest

1 "mid major" / borderline major in Alaska Airlines

1 "not a major, but not exactly a regional carrier" in Jet Blue

and a bunch of regional outfits like Frontier, Porter, Spirit, etc.

That's not to say that more competition wouldn't be nice, but it's hardly the case that there is no competition. Heck, as far as that goes, Peter Thiel uses airlines - and their razor thin profit margins - as the prototypical example of why "competition is for losers"[1] in his talks.

[1]: https://www.youtube.com/watch?v=3Fx5Q8xGU8k

With air travel the routes are the product. If there is a monopoly on the route, there is a monopoly. And a cartel situation with the carriers agreeing not to compete with each other on that route.