Though I agree with your broader point, if airlines regularly auctioned off seats right before a flight it would encourage customers to wait until such time to make their ticket purchase. Even if the actioned seat still net them some profit, the overall effect could cause a psychological devaluation of regular tickets.

I get that not every flight is equal, but nor are hotels, yet they have systems for blind comparisons.

For a plane ride, people are willing to put up with zero leg room, multiple hour layovers, red eyes, zero free bags, etc. just to save a few bucks. I think it's because the plane ride is seen as a means to an end, rather than part of the actual vacation or trip, so suffering for a few hours is palatable to most people.

The 1 cent paid ticket simply doesn’t (or shouldn’t) exist.

But if the plane crashes, even the $2k last-minute 1st-class short-haul ticket will be a massive loss after all lawsuits are settled.

If the marginal expense of a seat is $200, and you paid $1000, you may sit next to a discount flyer that paid only $250. And because of that, the flight may be net-profitable instead of net-loss.

But the moral of the story is it's not as simple as "selling the seat is always better".

The airline and first class ticket buyers needs the economy passengers just as much as vice versa.

With the existence of economy-only planes and lack of 1st-class only planes, I’d argue that the “cheap seats” are what makes aviation viable, rather than being a money-loser.

On a typical flight, the revenue probably follows a Pareto distribution--20% of the passengers (first class) provide 80% of the revenue--but at the paper-thin margins of an airline, you still need the other 20%.

Economy-only flights are usually from economy-only carriers, which trade even thinner margins for not having to worry about the annoyances of catering to first class passengers.

Economy conditions are increasingly terrible because cost-sensitivity and easy-to-verify sources of pain (nonstop vs. layover flights) have a greater effect on consumer behavior than seat size and other creature comforts. With these conditions getting increasingly worse, economy flights become increasingly more cost-effective, and perhaps it becomes increasingly harder to keep the pampered first class passengers on the same airline or even the same plane as the economy passengers.

Also, first-class tickets aren't even at the very top of the market any more than Audi and Lexus are at the top of the automobile market. The top of the market is in charters and private jets. An airline that flies planes only for first class passengers is close enough to a charter airline that they might as well become a charter airline and bypass TSA and the other associated miseries of air travel.

(Oddly, it occurs to me that European companies do a really good job of settling in the niche of "penny-pinching to the point of being kind of terrible, but such an amazing bargain you can't complain"--IKEA, Ryanair, Aldi, Lidl. Walmart felt bad about being terrible and tried to get a little nicer to compete with Target; Amazon felt bad about being cheap and terrible and decided to chase a membership model and set up a cloud computing business on the side. Maybe it's because America has a deep inborn cultural fiction of not having social classes and companies feel embarrassed about obviously not catering to the quintessential middle class American family?)

There are a few airlines that fly all-premium configurations on certain routes. Singapore does that on the Singapore-Newark route. British Airways does it on London City to New York. SAS used to on the Houston to Stavanger route.