For the sake of the discussion let's assume that all seats are in the same class (ie: economy) - there are no business / first class seats.
So the idea would be:
1. All seats are sold at the same price, no matter how early or how late you buy. The price covers all the costs associated with running this flight, given an expected "occupancy rate" (sorry not the right term).
2. All tickets are non-refundable. If a customer changes their mind, they use the airline app to put their ticket up for sale. They can try to sell the ticket at the same price, or at a discount (or maybe even at a higher price?)
3. Airline charges a small fee (something like $10) every time the ticket is transferred to another person.
Since this has never been done - to my knowledge - there must be something wrong with it. But I wonder what it is?