ya you failed to grasp the whole way a plane uses thrust, the trust is not coupled directly to the ground (like a car) it is coupled to the air. once you grasp this very simple concept you will realize how ignorrant you are
you said right in your post the prop on the plane is used to move the plane forward and it will do just that. and it will gain airspeed do to the thrust produced which will over come the minimal drag the wheels have.
the fact that the ground is moving is whats throwing everyone off, when in reality the ground speed really doesnt matter bacause the trust is not applied through it but only in relation to it
you could use an airboat in the same theoretical example altho the drag forces involved are greater between the boat bottom and water surface