As stated, you seem to be implying that selling a ticket for 1 cent is better than flying an empty seat. But that's not guaranteed to be true. If they put someone in that seat at a ticket cost of 1 cent, does it cost more than 1 extra cent in fuel to move the now-increased weight of the aircraft? If there's a free soda or something offered, does the extra one they serve cost more than 1 cent? Does the extra time it takes to board that passenger cost more than 1 cent? Does the sum of all of those things cost more than 1 cent?
There absolutely are circumstances in which flying the empty seat is better than selling that seat at the price the market would have borne. And we know this, because we know that airlines routinely fly planes that aren't full, instead of going to extreme lengths to auction off ever-cheaper tickets in hopes of getting someone in every seat on every flight.
(and that's without getting into the fact that not all seats, tickets, aircraft and routes are equal in terms of what they cost to operate and how much money they can make, and all the other things that go into the arcane art of airline yield management)