Actually, or those who actually get it, and agree that the plane takes off, here's a secondary question. Consider this statement in the original question:
The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
"Match the speed of the wheels." Speed of the wheels relative to the ground? Rotational speed of the wheels? Speed of the wheels relative to the belt?
Depending on just what is meant, I figure the wheels will just spool up to infinite speed, or the plane wil take off with wheels that are not rotating.