But you can't have it both ways. If they have to have lower fares in order to fill the planes at night, that indicates that there's less demand for those flights than there is for daytime departures.

The amortized cost of adding another daytime flight is much lower than the cost of adding a 3 AM flight would be. You've got to hire extra staff, and probably pay them more; most people don't want to work the graveyard shift. Then there are all of the associated personnel you're affecting -- you're asking TSA to stay open later; you need more hotel, parking, and rental car shuttles; you're going to want retail outlets to stay open later, at least in your hub; you're going to need to keep the lounge open later; etc. If all of the airlines were to decide, at once, to add 25% additional capacity by running 24/7 operations, it would probably work out. If one single airline tried it, you can expect that many of those additional costs would be passed along to them.

If HP's nighttime bank of flights were that valuable, they would have acquired AA, instead of vice versa. Oh, and you might want to tell Southwest that AA has a monopoly there. According to Wikipedia, AA's market share (CY 2017) at PHX is 46%; WN's is 34%. That's not exactly fortress hub territory. By comparison, at CLT, for June '15-June '16, AA got 91% of the traffic; at DFW, Dec '16-Nov '17, 68% (but #2 and #3 were Mesa and Envoy, each at 8%; I don't know if Mesa operates any American Eagle flights, but Envoy definitely does).