Soundstage and image height, does it exist?

This series of tests does exactly what the OP is looking for. 

Online LEDR™ Sound Test | Listening Environment Diagnostic Recording Test (audiocheck.net)

There are some people who honestly don't, won't and can't hear it. Everyone is physically and emotionally different.  But sometimes these people can't fathom that other people can. And some of those people think that it's their responsibility to tell people it's nonsense. 

@simonmoon I don’t know about the mastering process, but my recent experience with entry level gear may provide some insight. In the last 4 years, I started with KEF Q150 stand mounts on Monoprice Monolith stands. I didn’t know it at the time, but my soundstage and imagining was limited to a line between the tweeters--a 1 dimensional soundstage. I replaced the KEF’s with B&W CM9S2 towers. The line of a soundstage expanded to a wall, which was only 2 dimensional, being height and width. More recently, that wall gained some depth when I upgraded the streamer to the iFi Zen Stream.

Two channel mastering is likely very different from the object placement afforded by the new spacial audio music mastering. But I would argue that there is some way in which soundstage height does exist. I would guess that someone who argues that soundstage height doens’t exist is probably proceeding from a set of definitions from the spacial audio world. Probably just a definitional problem where people are talking past each other.

My understanding of human sound perception of height is that it occurs mostly in the pinnae, causing the tonal relations and phase relations to change at the eardrum. There are no timing or level differences that can give us height information so a two channel playback system doesn’t inherently have anything to work with. But we may perceive a ceiling echo in a concert hall recording as coming from above from other unconscious means of deduction. You could say it’s our imagination but it would be informed imagination. If a recording is made using a dummy head then tonal relations associated with height do get encoded onto a 2 channel stereo recording. All directions are possible, but it usually doesn’t work super well because 1. Our pinnae are not all the same, and 2. The sound goes through the pinnae transformation twice - once at the dummy head microphone and again when the sound from the speakers hits your pinnae. My experience with listening to dummy head recordings through speakers is that the height effect can make it through all these issues with powerful effect sometimes. I have a recording of airplanes flying over that creates a very powerful directly overhead effect on every speaker I’ve tried so far.

Any system that has a tonal response that mimics your tonal response for height can cause a height effect for you. Ceiling reflections can also create a height effect. And of course speakers up high can create that effect. My speakers tweeters are higher than my seated position so I have an elevated sound stage.

Image height is a function of the reproduction chain, loudspeakers in particular. If it was simply a matter of saying that there is no vertical information encoded in stereo recordings then the resultant sound stage would be non existent in the vertical plane.