why do expensive amplifiers produce a better soundstage

Are you a non-audiophile? I do not think so. Therefore, please do not make statements on behalf of non-audiophiles based on imagination.

Audio is full of myths. We’ve been trying to answer these questions. I solve few these unsolved questions. 

I was a core a’philes for >3 decades. Now I listen like a non-a’phile. I can alternate to be a’phile or non-a’phile. I choose to be in the non-a’phile ears because 1) my audio system a natural sound system (there’s no other), 2) a’phile life is pain (brain fog, dilate eyes, more body aches, never satisfied with music, requires lot more money, etc.).

My better half and my children are definitely not audiophiles, yet they can clearly perceive soundstage width, left-right placement, front-to-back distance, and even the perceived height of a singer. 

They might have a’phile ears due to mildly listening your system. But you’ll never know what they perceive is same as yours or not.

Spatial cue information can be recorded, mixed, and produced

I agree for spatial cue info. Recordings also contain distortion noises. SCI is not a distortion noise.  Alex/Wavetouch audio

What the heck does soundstage mean? I don't think many people really understand it.

... life is pain (brain fog, dilate eyes, more body aches, never satisfied with music, requires lot more money, etc.).

You’ve described my condition with remarkable accuracy. 

everybody knows that $10,000 interconnects produce the soundstage.

If we are going to include the room in the mix, we should also include the type of speaker since line source speakers are less influenced by the room than point source speakers.