You will hit max tire speed WAY before you get anywhere close to enough friction to hold the plane still (slack the rope in your experiment).
Once the tire flies apart the friction goes way up so it wouldn't be too hard to prove the plane won't fly as double tire speed at rotation for every plane over 10,000 lbs I've flown would be well over the limit. Most tires max out at 150 to 180 kts. If rotation is 120 then double is 240 and the tires blow.
With that said, that's not really the point. The plane on a conveyor myth is to point out that the conveyor does not hold the plane still. Most people lose sight of the fact that the prop pulls on the air to move the plane and the tire/conveyor contact is meaningless.
Take tires and axles out of it and use skies on a moving sheet of ice and you see my point.