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We are assuming "no slip" between the wheels and the runway. If you are stating that a plane on skis on ice will take off, I fully agree.

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In that case I'm a bit confused too. It's been a long time since I took physics, but as I understand it...

As the plane moves forward relative to the runway, the wheels also move forward, because they're attached to the plane. This generates friction between the wheels and the runway. This friction causes the wheels to spin faster (the current rate of rotation is irrelevant).

If the wheels spin faster at the same rate as the conveyor belt, then causing the conveyor belt to accelerate will not change the acceleration of the wheels relative to the conveyor belt. Therefore the conveyor belt can't compensate for the faster rotation of the wheels as the plane is moving forward. Therefore as the plane is moving forward the speed of wheel rotation changes relative to the speed of the conveyor belt and the assumption in the original post becomes untrue.

Can someone please point out exactly where this line of reasoning goes awry? I don't doubt that Patrick knows 100 times more about this than I do, but I would really like to know where the flaw is. Am I making an assumption that isn't warranted? Is my understanding of physics off? Where is the issue?