It's not a viable option for takeoff as it doesn't require a shorter amount of distance for take off. You're sort of missing the point. When the plane starts moving forward, the plane is at Point A. It's inertia is moving forward. The only part of the plane that is modified by the runway, isn't it's position at that point, but the wheels, there's a slight amount of drag created, but in fact the plane's forward momentum + the grounds momentum is additive on the plane's wheels (The planes wheels will spin faster).

However the distance necessary to accelerate to the take off speed will remain relatively the same, in fact being able to match the plane's take off speed would be near impossible, and cause more issues.

In fact planes on carriers, use catapults due to the amount of speed they gain. It uses vastly less space than any other type of takeoff, less mechanical danger, and compared to a conveyor the size people would need, or the timing required by a conveyor (if it even worked in shortening the run way) the amount of power consumption for it would be astronomical. The idea that a conveyor would in any way benefit a takeoff compared to a catapult (rubber band?) is a bit silly.

I honestly think people aren't getting both the limited wake the prop would generate, and the fact that the wheels are magical friction material. As there's no Drive train on them, they're able to spin at what ever speed is necessary.

But let's assume you are right. Why don't pilots have giant fans to launch plans? Or why not make a plane with a giant fan, that blows air over it's own wings? These ideas just don't work in reality. Not at any efficient rate. I imagine someone could make it work, I'd definitely like to see an ultralight taking off that way.

For a practical demonstration of of the wheels issue, Take two objects. A wheeled car (or any cylindrical object.) that doesn't have a drive train or brake, and either a wheeled car that has a drive train attached (that can be set into drive) or just any non wheeled object. Put a sheet of paper under both objects and pull the paper out and look what happens to the two objects.

Newton's laws at action. A object at rest stays at rest until a force is exerted at it, but wants to remain at rest, so the wheels turn, but the vehicle doesn't move back at the same speed of the paper. because the wheels are able to turn freely. The second object with no wheels or a wheel in gear will move faster in the direction of the conveyor (potentially not the exact same speed as the paper but more of the energy is transferred depending on the surface material used)

Add in thrust (not through the wheels) at the same speed as the paper? And what would happen to the two objects? The first object would move forward, the second might start moving forward at a very slow speed or stay "still".

The first object would start getting air flow, as it's moving through the air, and that's why it actually is possible for a plane to take off.

Btw I do believe it would be possible to stop a plane from flying. But to do it through the wheels would be remarkably inefficient, and to do it another way require essentially a string. A plane tied to a stake or pole would not take off. (assuming it's already at diameter of the rope and aimed away from the pole.) But the example of a conveyor would only work in theoretical terms, because the numbers and speed of adjustment would be far beyond what anyone can do.