The point is that the second ANY force is applied to the plane, the wheel speed jumps to infinity. If there is any delay in the spin-up of the treadmill and wheels, the plane will move which violates the premise that the treadmill will accelerate to match the wheelspin. If the plane is moving, then the treadmill must be moving slower than the wheels are spinning, which violates the whole premise behind the question. And it still results in the wheels and treadmill moving at an infinite speed. Which isn't possible.
The situation described in the question is impossible. There is no way the treadmill could ever instantaneously match the wheel speed because the instant the plane moved forward through the air, the wheels would be turning faster than the treadmill was going, which violates the premise behind the question.
So everyone but HT was wrong
