Phillip Longman and Lina Khan at Washington Monthly blame airline deregulation for high cost, low frequency flights between less-travelled American cities. Some cities are losing major business headquarters because of poor flight logistics. They recommend a return to airline regulation with cross-subsidization of low-volume routes. I'd be awfully surprised if that fixed things.
As best I'm aware, Air New Zealand is under no mandate to provide cheap travel between smaller New Zealand ports of call. So as a quick test, I checked the price on Air New Zealand for travel from Christchurch (population 330k or so, South Island) to Napier (population 100k or so, North Island) for a month from now. They're quoting NZ$273 ($218 US) round trip with no connections. There might be cheaper flights; I didn't check any aggregators. A shorter (about two-thirds the distance) hop within the US, Pittsburgh to DCA, for the same dates, is US$374 (including $43.21 in taxes and fees) on Orbitz with a stop in Boston. In real terms, the shorter US flight costs more and is less convenient. If I want a next-day flight, the NZ round trip is NZ$642 (US $514); Orbitz has the PIT-DCA route at US$635.
If you change things to American cities that are more comparable in size, like a routing from Toledo, Ohio to Erie PA, the New Zealand advantage gets a fair bit stronger: the next-day flight between those two is $1000 US and has two stops. Maybe there's just something weird about the airport combinations I've picked; they were random draws based on rough city size.
Point-to-point domestic travel within New Zealand has lots of small planes going between lots of small places, as well as a few higher volume routes with bigger planes. And, in general, it's a joy: rock up to the airport 20 minutes before your flight and walk straight onto your plane after waving your phone at the machine at the gate. If you have checked baggage, add another 20-30 minutes to be safe. When the weather is clear, just watching the mountains out the window is almost worth the price of the airfare.
So, if deregulation is the problem, why is flying within New Zealand relatively cheap? It isn't going to be fuel costs: I'd expect that domestic air travel attracts carbon charges via our emissions trading system. And small-country maintenance and engineering costs have to be higher: engineering works have a big fixed cost component, though I think AirNZ has outsourced some of that work.
Further, whatever subadditivity and network problems might require network regulation in the US ought to apply doubly hard in New Zealand, where Australian airlines can cherry-pick whatever higher margin NZ domestic routes they like. Cabotage is forbidden in the US, but flying is less expensive here.
If I had to point a finger at anything in the States, I'd start with airline security. You get enough stories about TSA agents making 4 year old kids cry, or stealing money from 95 year old war veterans [or allowing that the money be stolen; who knows what happened], or molesting women, and people don't want to fly. Lengthy security-induced queues at airports add a fair bit of time to your total flight cost. So more people choose to drive. That sucks in industries geared up for bigger passenger volumes that now have to spread those fixed costs across a smaller number of fliers. Worse, airline security measures increased the fixed costs of flying at the same time as they reduced the number of travellers over which those costs could be spread. New Zealand lets small airports provide low cost services.
Want cheaper flights and better service within the US? Look at airport slotting fees, cabotage rules, and security arrangements before putting in price and route controls.