Can you name any? There may be routes where F routinely is filled with upgraders, but I suspect not many (if any) where F routinely goes out with available seats.

Look, the OP does raise a valid point, but it's not as simple as the OP suggests. The airline does need to maintain the integrity of its pricing system (I know that sounds like a joke when we're talking about airlines) and loyalty program; taken to the extreme, the OP's argument would suggest that AA should auction off all empty seats rather than fly them empty (assuming, of course, that the high bid at least covers the incremental fuel cost of carrying the passenger).

You can be sure that AA monitors data points like how many F seats fly empty and how many F seats are awarded to upgrades rather than sold. And certainly AA considers strategies to maximize revenue. It's silly to suggest that just because they don't do it in the way the OP suggests they are making bad business decisions.