You just contradicted yourself. Either you end up at windspeed - which means zero speed relative to the air, which means the cart stays at fixed position on the treadmill - or you go slower. Make up your mind.
Of course you'll be wrong either way. You can't seem to understand that the motion of the cart is not powered by the wind alone, it's powered by the difference between the speed of the wind and the speed of the ground. That difference has nothing to do with the speed of the cart, and (in principle at least) one can always extract energy from it.
Well, I am truly benighted. If cart is said to be at windspeed when on the belt, and the propellor is in the air. If I get out of the car, I should be blown into the propellor. You model fails to predict this admittedly foolish behavior.
Perhaps you can enlighten me.
To anticipate your objection, you told me that the wheels are the ground.
So, if I hang my legs out of the car, and onto the ground, I will be subjected to torque, rather than the linear motion that we mortals would expect.
Try as I may, I still can't understand why there is wind blowing over the propellor, but not when I put my hand out of the window.
The only thing I could think of is that the belt might be the wind, but you say not.