A plane is defined as a flat two dimensional surface. You will notice that the definition does not include or define a tilt or radial orientation of that plane within a three dimensional space.
Therefore a plane can be in any orientation. It can even be parallel to the ground with the cast being sidearm. If you are standing on a high bank, or an elevated casting boat platform, the rod could be tilted way down with the plane on the tilt of that cast.
Secondly, one of the key points to an efficient cast is to have the rod tip move in a SLP or a Straight Line Path. A Straight Line by itself does not define the plane it lies on. A straight line in a three dimensional space can lie within an infinite number of planes that rotate round
I wrote a rely to a question about tailing loops on another fly fishing BB that further explains the vertical plane casting stroke as the foundation for other casts.