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I'm no physics expert, but I think I have an example that might satisfy Nasty/Crazy/goofball.

Imagine that there is no friction at all involved with the wheels and the conveyor belt. The wheels and the belt are moving at the same rate, but this is not necessarily because of friction.

Imagine that the conveyor belt and the wheels are both completely stationary. You expect the wheels to spin faster as the plane moves forward because of the effects of FRICTION BETWEEN the wheels and the conveyor belt. If there is no friction, then the wheels will remain stationary - regardless of the speed of the plane (and, incidentally, of the conveyor belt).

This is a specific hypothetical situation in which the plane clearly accelerates under the conditions outlined in the OP (there is no suggestion that the identical speeds of the wheels/belt are due to friction).

I'm not 100% sure how this situation works if the speed of the runway and wheels scale linearly due to friction, but I don't think it's relevant. Even if we imagine the speed of the wheels and the speed of the conveyor belt to be completely independent (they just happen to be identical), the principle of the solution stands.

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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.