A treadmill wouldn't help the plane take off. What Mythbusters showed was that it's not a hindrance to the plane, because planes don't need ground traction. They do need to be moving forward, relative to the air they're flying through, in order to generate lift. A treadmill, if it pushed the plane backwards, would not allow it to take off "in place", and actually the fact that a treadmill wouldn't push the plane back is the whole reason a plane can take off on a treadmill.
Or to put it differently, the only treadmill an airplane could take off on would be the length of a runway.
They certainly do. First, they need it to get the pointy end airplane pointed in the right direction. Then, they need it until they are going fast enough for the rudder to work.
Mythbusters didn't get it. The whole point is for the treadmill to accelerate so it could exert a force on the wheels due to wheels' inertia. Sure that kind of acceleration is somewhat unrealistic, but ignoring the task conditions is just bad.
Most people wrongly believe that the situation is similar to that of a car on the highway. If a car is capable of going ~80 miles per hour, and you put it on a treadmill going 80 miles an hour in the other direction, the car will run in place on the treadmill. The takeoff speed of a jet is something like 160 mph, so the picture most people have is running a treadmill at -160 mph, and they picture the airplane running in place just like the car. As Mythbusters showed, that's not what will happen, the plane will just move at 320 mph relative to the treadmill.
Of course you could imagine a situation that's not analogous to the car at all, in which we just dictate that however fast the treadmill needs to move to exert a force on the jet equal to that of the engines, it will move that fast. That means we've defined the situation in just a way that by definition, the airplane will not be able to move forwards. What most people don't realize, though, is that doing this is not like stopping the car on the highway. In fact the force exerted by the ground on the wheels during takeoff is so small that to effectively stop the plane, you'd have to spin the treadmill fast enough to destroy the wheels and carriage. And maybe even that wouldn't do it!
A car capable of 80 mph, assuming some gearbox/rpm headroom, will jump off the 80mph treadmill too, normally there's a lot of drag to overcome which isn't there on a treadmill.
The second paragraph checks out: with a realistic plane on an unrealistic treadmill either the wheels will fall off or the treadmill will produce enough airspeed to lift off the plane vertically up.
I suppose if the wheels were large enough cylinders then they could provide lift as well, although they would need to be spinning in the opposite direction.
Or to put it differently, the only treadmill an airplane could take off on would be the length of a runway.