Because the amount anyone would actually pay is substantially below cost for most routes, but it's still a service that many people depend on (either directly or by the indirect economic impact of travel). It's a genuine force multiplier that is unaffordable without being subsidized; making it a utility would just shift the subsidy from credit card points programs to the government.
If airlines didn’t exist, people and goods would continue to move around the globe as they have done for thousands of years. There’s nothing magical about air travel (or any other transport mode) that makes it worthy of subsidy .
> the amount anyone would actually pay is [...]
That's.... like a pretty shocking erasure of the idea of a demand curve given the forum here.
To be glib: no, that's not how it works. Increase the price and fewer people will fly, but the demand won't drop to zero. Decrease it and you make less money per ticket but the size of the market is bigger. At some point there is a local maximum, to which the market seeks.
But conditions change occasionally and the equivalent supply curve is moving rapidly because of the oil shock (i.e. it's more expensive to put planes in the air to service tickets you already sold). And things like the mess with Spirit are what happens when the market readjusts: the rest of the industry will (probably) backfill some of the lost capacity, but not all of it, and prices will (probably) rise a bit to a new equilibrium.
> Because the amount anyone would actually pay is substantially below cost for most routes
This is absolutely not true. If all the airlines were prohibited from making money with anything else (miles, credit cards) then airfares would rise across the board and there would still be plenty of demand. Not as much, but still plenty.