Well, this might be less relevant when in many countries there are cheap airlines, but the logic you're describing is the one that lies in the base of all the last minute travel agencies.
If you wait long enough, these companies offer you cheap tickets to flights about to take off - there are vacant seats, and they rather sell them for cheaper prices than keep them empty (most of the times they'll even offer you a cheaper ticket on a 2-way flight).
Most of the contact customers have with these last minute travel agencies is through the phone or a website. However, many of these agencies have airport offices, where you can get REALLY last minute tickets, and that's where the cheapest deals are made.
Note that it's irrelevant to flights with high demand, since there are long waiting lists, and they tend to fill the aircraft without much problem even if a passanger cancels in the last minute.