No, the math works fine. Ignoring baggage fees and first class vs catch etc. If you have a flight with 300 identical seats and you could sell everyone single one of them for say 100$ and that’s your maximum possible revenue from a single price point. Now the question becomes how do you capture value from people willing to pay more than 100$? You can play some games with round trip tickets and minimum stays, but again let’s ignore that and just focus on the ramp up.
If you designate say 75% of your ticks at a lower price of X then some people willing to pay more will just buy at that price. Essentially the trick is to minimize people who are willing to pay more who end up buying cheaper tickets. And it turns out people booking close to the flight are generally willing to pay more. Sure six months out they still sell off up to 75% of tickets at ~100$ raising or lowering prices based on demand so their losses are limited if nobody else buys the ticket the flight is still mostly full. But at that 75% they start the ramp up and they also ramp things up as the flight gets close.
2 weeks out they say all tickets are 200$ even if some of those 75% are unsold. At the last day bump it to 400$. If over 1 month we can ignore seats at 100$ because that’s unchanged. Sell 1,000 seats at 200$, and 500 seats at 400$ and fly with say 1500 empty seats that’s 400,000$ where you would only make 300,000$ if all 3,000 seats where sold for 100$. But what if they dropped prices at the last hour? Well most of the time they have empty seats so many would avoid the 400$ ticket and would tend to wait around for that window especially for flights from A to B leaving every hour. Peak prices are a game of chicken and they can’t blink or they lose billions in revenue.
This is of course heavily simplified but it does demonstrate the basic trick I am talking about where they extract value from unsold inventory.