The no-show has paid for the seat and is unlikely to be refunded. The airline still has 100% income.
Wrong assumption. The no show was most probably a high fare flexible ticket passenger who decided to change travel plans and take another flight. Revenue went to that other flight, and this one left with an empty seat. Overbooking is done to ensure that this empty seat is filled.
Overbooking is a very complex art and if practiced correctly (usually by computer forecasting models that are specific to each and every flight) then the flight leaves close to full, with no denied boarding. I know of several routes where one must apply a 15-20% overbooking ratio and the flight will still departs with some empty seats.
Low cost airlines do not overbook, because their fare rules do not permit any change, and revenue truly stays with the airline on that particular flight even if the passenger elects not to fly.