I can tell you why the airlines would be planning on having empty seats in practice - because there are sometimes literally not enough people interested in travelling to fill the aircraft, so they adopt a strategy of leaving empty seats because they have no other option. If you've ever flown some god-awful connecting flight at 2am you might have seen that in action yourself. But that isn't because the airline is choosing to reserve seats, they'd much rather have more passengers - that just isn't an option.
How and or when exactly to you plan to sell those tickets?
Do it after the price hike and people will just wait.
Do it before and you need to see the future to know how many seats will eventually be sold otherwise you just traded a 400$ ticket for a 100$ ticket. It’s no more a viable option than suggesting it’s easy to win the lottery just pick the correct numbers.
Your strategy has the same problem - you have to predict how many last minute travellers there are too. If you just leave an unnecessary buffer then the strategy fails. The one of us who does a better job of putting exactly 100 bodies in 100 seats - none left over - is going to have a more profitable airline. That is somewhat core to the argument us pedant capitalists make.
It’s just the math works out so on the margin having even slightly better than a 1 in 4 chance of selling at 4x the prices is a net gain. Suppose their reserving 50 seats and have a 26% chance of selling all 50, only a 50% chance of selling 20 or more.
That means on 1/2 of flights their intentionally flying with 30 or more empty seats, but reserving even 49 seats rather than 50 loses them money.
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.