The answer is in the original problem. It is stated the conveyor belt will match the speed of the wheels.
Pedantry aside this is often read to mean the belt will run backwards as fast as the wheels turn forwards. In that case the wheels will have a rotational speed at the highest at twice V1 where the plane will take off. That is fast, but within expected tolerance of the wheels. No problem.
Now the pedantry, but the relevant kind. Speed of a wheel can mean two things: rotational speed and directional speed. And if you mean directional speed, the frame of reference is important, even here. An often made mistake in this debate: confusing the two. Rotational speed is a completely different beast from directional speed, you can’t compare the two. That is what I did in the previous paragraph and is really wrong!
This is very basic engineering and physics: State clearly what unit is what in SI units and define a frame of reference as soon as motion and directional speed is introduced.
Rotational speed is plain (heh) silly as I will explain below so let’s look at directional speed first. Simple: Vwheels=Vplane. The wheels are bolted to the fuselage. Same Speed! I know they can spin, so what? Rotation is not directional speed. Knots or m/s, I don’t care but not degrees per second.
Now the conveyor belt is going to match that, so the surface will match the speed of the wheels which is the same as the speed of the plane so the belt will roll forwards (match) with the plane so the wheels never even turn. (OR run backwards and max out at -V1 but that is not what the problem states. Match=equal, not counter equal).
Oh, and about reference frame? The above both works if you observe speed from the plane (Vwheel=0, remains 0, they are still bolted on.) or from an observer standing next to the runway. But if you define speed from a surface point on the belt … the belt will again run forward to match the speed of the plane and neither will move ever from the point of the reference frame.
The plane will still take off because from that reference frame the air will now speed backwards creating enough force to lift off at V1 airspeed 
Obviously from an observer on the ground the plane will also have groundspeed. Relative motion is fun that way…
Rotational speed leads to weirdness. The moment the plant accelerated forward (By engine thrust working on air, nothing to do with the wheels) the wheels will start to turn and the conveyor will rotate backwards to match that speed. In that case the belt will accelerate the wheels even more and could never match the speed of the wheels since they are also accelerated by the plane’s motion.
So matching rotational speed is impossible. The wheels will always have a higher positive rotational speed than the belt since the wheels are also moved over that belt. That means the condition of the original problem can never be met if speed is read as rotational speed so that cannot be how the problem should be read.
AND ANOTHER THING: You mentioned the effect the belt has on air? If the belt runs backwards (As most people assume…) it will drag the air backwards creating a headwind reducing V1 groundspeed… It will help the plane take off. (And might make it crash immediately when it parts with this localised air stream. Don’t care, it took off )
