why do expensive amplifiers produce a better soundstage

There is no such thing.  Price does not play music.  Price does not generate soundstage.  Get real.

Everything in your chain, speaker placement and room matter.

@toddalin 

everyone thinks their system sounds better than anyone else’s. 

If you have two systems where: speakers are capable of imaging well; room is reasonably controlled; source quality is high; listening position is stable, and both amplifiers are of equal design quality, then I believe that the one with better parts quality (which usually equals being more expensive) will tend to destroy less of the signal and therefore produce a better soundstage. If you just take one part, say power supply, a better power supply which leads to more stable current delivery can have a significant  impact on soundstage. 

@yamaho 

There are low cost amplifiers that produce incredibly large 3-dimensional sound stage.  

A Rogue Audio Cronus Magnum amplifier for example can deliver an exceptionally large holographic sound stage- provided your speakers are set up correctly for your seating position and are well designed for coherence and wide dispersion. 

Expensive amplifiers with higher power output can sound bigger because of the additional power.   

@ronboco 

You are welcome to come by and judge for yourself.  I am in Orange County, CA.

While a Youtube video can’t convey the soundstage and imaging (much is lost in the recording process and it depends on your own playback system), you can hear the clarity and detail.

The speakers were designed and tweaked in the room for the room over years of listening and there is no eq or room correction, either electronic or physical being used.

https://youtu.be/OmWNOi6b4ak