Selling tickets at a discount would be a good idea if you're thinking about profit maximization for that one singular flight on that singular day.

But CO and other airlines seem to believe that the long-term downside outweighs any lost revenue from the sale of last-minute discount tickets.

Possible sources of the downside:
- Reduced ability to lock in partial capacity utilization with pax buying early and cheap (they would just wait)
- Continual reduction in ability to lock in partial capacity until you have almost no capacity filled until the last minute (you train pax to buy at the last minute)
- Inability to get $$$ from people who really have to get to their destination on short notice (the people who have the most inelastic demand)

The people who have to go somewhere and know they have to go there far in advance exist....but I'm guessing they make up a smaller portion of the people willing to pay $$$ than those who have to go somewhere, like, tomorrow.

Last-minute discounting does happen (e.g., priceline) but note that it happens only in separate channels catering to the extremely price-sensitive and schedule-flexible customers.