Just a thought, Paul, because you are hung up on the wheels failing -

In the original scenario the plane (of no specific type) is sitting on a treadmill of infinite length.

So why are you hung up on the practical problem of the tire rating but choose to totally ignore the pratical problem that the treadmill in the scenario can never exist, because the belt for the treadmill would have to be twice the length of the treadmill, and since 2x infinity can only equal infinity if 2 is equal to 1 (which it isn't) the treadmill in the scenario will never really exist.

If you want to nitpick, why don't you assume the plane is a wooden antique which has been exposed to the elements and termites and which, because fo the structural damage from time and exposure, preceeds to fall apart from the engine vibrations?

Yes, in the real world, the tires might fail before the plane takes flight, but that's really not the essense of the myth.