Penguina
They already have this and have it in production.
The belt is running at about 15-20 knts and the fan is anywhere between 0 and 50knts of wind.
Its called an aircraft carrier
Actually it doesn't matter what speed the threadmill is doing the only thing the aircraft carrier is doing is steaming into wind to get the intial airspeed up. The relative speed of the ground under the aircraft wheels will have no relation at all on take off distance presuming no friction.
PS it really is quite amusing seeing how none engineers think the world works. How effects which engineers instictively ignore are given huge weighting and how complicated very simple engineering systems become.