why do expensive amplifiers produce a better soundstage

If you had the experience, you'd find that it's not actually the case.

A simplified. Answer much higher quality parts including much bigger,better transformer,and power supplies and much bigger capacitance ,$$ for roughly only 20% of the  goes into the build . I owned a store for a decade , and plenty of things 

not disclosed, cables by far the biggest mark up.

The higher the price, the nicer the nice.

I would suggest that with “more expensive amps” , one has also heard that amp connected to “more expensive” components, speakers and cables, and likely in a room that has had some work go into it, at least into seating and speaker placement. That all matters. I would suggest that if one were to do an A/B test with a “less expensive” amp and an “expensive” amp with all other factors the same, and both amps had the same power ratings equally driving the speakers well that no one would be able to discern the difference in a blind listening test.  

Why do expensive amplifiers often produce a better soundstage?

They don’t create soundstage — they preserve spatial information that cheaper amps partially destroy.

Soundstage depends on extremely small timing and phase cues between channels, plus very low-level ambient information (reverb tails, decay, hall reflections). Less expensive amplifiers often blur these cues due to phase shift across frequency, power-supply modulation under real speaker loads, higher noise modulation at low signal levels, and reduced channel separation when driving reactive speakers.

Higher-end amplifiers typically have:

• Better phase integrity and time-domain behavior
• Lower noise and better low-level linearity
• Much stiffer power supplies (less rail sag and micro-compression)
• Better channel isolation and grounding under load

The result is not “added” width or depth, but less smearing, so images stay stable, depth increases, and the stage feels more continuous and believable.

In short:

The soundstage is already on the recording. Better amplifiers simply get out of the way.

It’s amazing that this issue seems to come up over and over again.