how to make a plane's height be Y instead of Z

By default, Unity creates planes normal to the y-axis. So that if looking thru the default camera the x-axis can be thought of as the width of the plane and the z-axis is the plane depth.

If I rotate a plain -90deg about the x-axis, this will make no difference as far as scaling goes: x will still be width and z will be what I’d think of now as height of the plane. First I thought I was misunderstanding the frame of reference for the plane’s transform and so I created an Empty merely as a parent transform; I added the plane with its transform set to identity as a child of the empty and then I rotated the empty about the x-axis by -90. But still the same result: I have to use the z-axis for the plane’s height / width or however we might want to call the other dimension on the plane along with x.

In contrast, this is not the case with a cube object: rotating it about the x-axis by increments of 90deg does alternate between y and z.

So am I missing something or is it just not possible because, say, it was decided that a plane has absolute coordinates?

You can use the new Quad game object. A Quad is a 2 triangle plane oriented on the XY plane with normals facing backwards (i.e. towards the camera if the camera is in its default negative ‘z’ position looking towards positive ‘z’).

Another solution is the CreatePlane editor script you will find in the Wiki. It allow sfor both horizontal and vertical planes and allows you specify their world size and (indirectly) the number of triangles.