Your problem, mr engineer, is that you seem to be measuring the plane’s speed the same way you measure a car’s speed… via the rotating wheels. The definition of speed is distance/time, not “how fast my wheels are turning”. If you’re dealing with a moving surface rotating wheels are not a true indicator of speed. It is used in cars because 1, the ground under a car never moves, and 2, under most situations there is no slip between the tires and the ground.
Quick example to explain “speed”. The roads are icy, and I’m driving to work in a 30mph zone. I’m going 25 mph, not spinning my tires, and see a cop running radar. I give it some gas, my tires spin, and my speedometer says 50 mph. My true SPEED is still 25mph, as shown on the cops radar, and the fact that in 1 hour will be 25 miles from where I am now. Wheel rotational speed is just an easy way to measure distance/time in a car, but as in this example and the plane example there are times when it is NOT your actual speed.
The original question said the conveyor matches the plane’s SPEED, but in the opposite direction. If the plane is going 100 mph, it is sending 100 miles of air over the wings in an hour. The conveyor is running 100 mph in the opposite direction, but since the plane isn’t bolted to the conveyor, it is still moving forward relative to the air. The wheels are going 200 mph and may explode if they were designed for a plane that takes off at 100 mph, but that’s not a concern in hypothetical physics debates.
Lets say the plane needs 70% thrust to get airborne on a traditional runway with no wind. To counter the slight rolling friction generated by the wheels having to turn twice as fast on the moving runway it might need 75%, but it will still fly.
Here’s one you can try at home if you have any toy cars. Place a big piece of paper on your kitchen table. Place a toy car who’s wheels rotate freely in the middle of the paper. Now pull the paper out from under the car as fast as you can, in a straight line, either directly to the front or rear of the car. The car will move, but only slightly. No where near as fast as you moved the paper though because the free rolling wheels allowed the paper to move under the toy. Attach a rubber band to the car, pull it slightly taught, and tie a string to the car to hold it in place. Have a friend cut the string at the exact moment you yank out the paper in the opposite direction the rubber band is trying to pull the car. I don’t care how fast you remove the paper, the car will still move in the other direction. It is getting it’s force from the rubber band, much like a plane gets force from the prop. Now remove the rubberband and replace the car with an RC car, driven by the wheels. Since the wheels make contact with the paper you can negate it’s forward motion through the air by matching the speed of pulling out the paper.
EDIT:
And seriously, if you’re designing airplanes for Boeing, I’m going to make sure I only fly on Airbus planes from now on