There is this widespread notion out there that FF award seats cost the airline little because they are 1) seats that would have gone empty anyway amd 2) trips that would not have been taken but fot the award seats.

This notion is wrong... I personally have never taken an award flight that wasn't quite full, and the majority of them have been oversold flights for which volunteers have been sought. FFs earn miles flying between LGA and ATL, ORD and DFW etc., but they do not redeem miles for these kinds of flights.