Maybe in the US it isn't sustainably profitable, but there are plenty of examples overseas where airlines remain profitable, even in bad times.
The one thing I've seen that the cyclically profitable airlines share in common is a high degree of unionization. They're stuck with unionized employees and have little ability to outsource.
Then there's carriers like VS, SQ, CX, JL, and LH. They run great airlines, but rarely have their own ground employees, even in their hubs --- instead, they outsource everything on the ground (call centres, check-in, ramp handling, maintenance, premium lounges, baggage service). That lets them focus on the safety and service aspects of running the airline. I'd be willing to bet that the carriers mentioned operate with a quarter of the permanent staff that it would take for a US airline to operate their network...
Not coincidentally, those airlines get some of the highest marks for quality, and have pretty decent safety records. So, the usual insults over "you get what you pay for with the lowest bidder" and the evils of outsourcing don't quite hold up there.