If the treadmill theory worked they'd have them on aircraft carriers. As alluded to above the treadmill is just a rolling road, the plane would have to increase power just to stay on the same position on the treadmill, even if at full power the plane is still staying in the same position on the treadmill but it is stationary in terms of the surrounding air blowing across the wings which provides the lift that an aeroplane requires.
The only way the treadmill theory would work would ne to have a giant fan blowing air at the plane to provide sufficient lift , you could then in theory get the plane to be effectively flying in a stationary position.
Right - well I'm not going to mention it again anyway !