The problem here is really selling all seats for the same price.
Airlines know that some customers are price-sensitive, e.g. those planning a trip months in advance, and some customers less so, e.g. business people flying out to a last-minute meeting.
So if they just sold all the tickets for the "average" price, they simply wouldn't get as many customers, because all the price-sensitive customers would go to their competitors still doing things the old way, and there's no guarantee that they will attract enough of the less price-sensitive customers, unless they lowered prices even more than the previous average, and if they actually make less than the current average price, this is simply not a viable plan.
In addition, since the customers you have left tend to book later, you won't know for sure if you're filling up your plane or not until closer to the departure date, and that could potentially wreak havoc when allocating planes to routes.
Airlines know that some customers are price-sensitive, e.g. those planning a trip months in advance, and some customers less so, e.g. business people flying out to a last-minute meeting.
So if they just sold all the tickets for the "average" price, they simply wouldn't get as many customers, because all the price-sensitive customers would go to their competitors still doing things the old way, and there's no guarantee that they will attract enough of the less price-sensitive customers, unless they lowered prices even more than the previous average, and if they actually make less than the current average price, this is simply not a viable plan.
In addition, since the customers you have left tend to book later, you won't know for sure if you're filling up your plane or not until closer to the departure date, and that could potentially wreak havoc when allocating planes to routes.