We already see this with how airlines alter the pricing depending on when the ticket is bought and whatsnot (because if it is bought for a middle of the week trip etc, it is likely to be a business trip).
You'd still likely need an auction system on top of fixed A-to-B prices, since first-come-first-serve might not be the most optimal system for holiday travel.
Surely the infrastructure owner can offer whatever pricing structure they like. Per-seat fees aren't exactly rare in private industry contracts either.
As the presentation above suggests, this would have a problem with, well, staying profitable. Tourist air travel is so heavily underpriced that you can barely tank up the jet with what you collected from people. That's one of (or maybe even the) reason for such variety in ticket prices.
I don't think it is unreasonable to purchase 4 or 10 seats at cost, but if you are considering buying 2 thousands, wouldn't you try to negotiate something?
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