Imagine you're in the center of a flat square rectangle. If you look North you'll look at an edge. If you look Northeast, you'll see a dot representing the corner connected by two edges- the horizon.
Now the distance of that corner is not relevant, you will always see a straight line with a dot representing the corner.
Apply this to a cube: if you're in the center of a cube, the corners are always in the same location, no matter how big that cube is. So the 'look' is not changed by the size of the cube. Since the skybox moves with the camera- you're always in the center of that cube.
The only reason for a bigger cube is the clipping plane. You want the gameworld to be INSIDE the cube to be visible. Thus, the size of the cube is only relevant for the clipping part not the 'looks' part.