The only way the treadmill can match the speed of the wheels is if there is absolutely no thrust acting on the plane. If the treadmill is moving, and there is no thrust on the plane, the wheels will freely rotate at the exact same speed as the treadmill and the plane will move nowhere. The moment you apply any thrust to the plane is the moment the plane starts moving, and then the wheels start rotating faster than the treadmill at a speed of the opposite speed that the treadmill is moving plus the speed that the plane is moving.
Help me out here. A plane can not move without thrust. Without thrust, it would sit there motionless, the wheels do not move the plane forward. The treadmill would not be moving until thrust is added, and as long as the treadmill matches the speed created by the thrust, the plane would remain stationary.
Again, I am thinking of the effect that gravity has on the plane. The gravity acting on the plane causes friction with the surface that the plane is sitting on. The purpose of the wheels is to conteract the friction. Imagine trying to go down a runway without wheels, the amount of thrust that you would need would be incredible. Now imagine that the ground (treadmill) moves at a rate equal to what is being generated by the thrust of the engines. Without forward movement, gravity and friction keep the plane on the ground.
Is your argument that there is no way for the treadmill to keep up witht the force of thrust? Is your argument that the thrust of the engines would give the plane lift and therefore overcome gravity and friction? Or is there something else that I don't understand?
My argument is that it does not matter how much thrust there is, without airflow over the wings, the plane will not lift off. As long as the ground beneath the plan is matching the speed that the plane is able to make the wheels move at, there would be no airflow over the wings.