In theory, moving edit points would be an excellent way to edit a curve, since they lie on the curve itself. Unfortunately, it doesn’t work out that way. This is because the shape of the curve determines the positions of edit points, not the other way around.

Maya does allow you to move edit points by “reverse engineering” the curve from the edit point. When you move an edit point, the Move tool tries to find a curve which passes through the new edit point location.

Because this process is time-consuming and has an infinite number of solutions, the tool must place constraints on how moving the edit point affects the curve. Because of these constraints, you usually cannot make major changes well by moving edit points. Moving edit points is best for small scale reshaping.

Even though it is slightly less intuitive, the only way to reshape the curve with complete power is by moving CVs.