Does high volume collapse soundstage depth?

If you have a room that's too reflective, or too reflective in certain bands this can happen.  The lingering notes alter the perceived soundstage. 

Of course, speaker compression is a real thing.  That is, the frequency response is not the same at every volume. 

Not necessary.  A higher-end system in a well-treated room will exhibit lower distortion, less amplifier and speaker thermal compression, and better control of room reflections. As a result, it preserves spatial cues, imaging, and soundstage depth much better at higher playback levels.

Always treated the volume control like the dial on a telephoto zoom lens. The more you zoom out the shallower the depth of field. In any room there is a specific distance from the speakers and volume for a track that renders the best soundstage depth. 

Actually, I find that it is low volume that hurts the soundstage.  The volume needs to be loud enough for the music to "immerse" you to get a really good soundstage and imaging.

Above that, it just gets louder.

High volume can have a negative effect. Typically when it reaches a volume where room reflections start interfering with the soundstage. You can increase absorption around the room and allow it to play louder with less interference. 

But in addition the better the system, the less loud it needs to be played to be satisfying. I remember, long ago I would play my system at reduculous volumes to get satisfying bass and dynamic range. Now with my system it is completely satisfying at 65db... if I am rocking out 75 db... although it plays without distortion at 95db... its just not necessary, I have a large well dampened listening area.