The answer is because an aircraft doesn't power its wheels at all. Its turbines compress air and force it out the back in order to propel the aircraft forward - so it is pushing against the air in the atmosphere and not against the ground. The wheels are just there to provide a nearly frictionless surface so that the aircraft can roll along the runway unimpeded. It is for this reason that an aircraft can take off on water or ice while a car (which turns its wheels in order to move) would not move at all due to the lack of traction between the wheel and the surface.
Assuming there is next to no friction between the wheel bearings and the aircraft, the wheels can roll independent of the velocity of the plane. The aircraft will, to a bystander, proceed along a normal takeoff roll (same distance), but the wheels at the point of liftoff would be spinning twice as fast as they normally would to account for the motion of the conveyor belt.
Hypothetically, if the aircraft's brakes were applied and the conveyor belt was switched on, then the aircraft would move with the conveyor belt as the wheels are not free to turn relative to the aircraft.