why do expensive amplifiers produce a better soundstage

Perfect explanation.

 Soundstage is an acoustic and psycho-acoustics   concept not an engineering one ...

It is not an amplifier who create soundstage but the system/room/ears-brain/body location...A piece of gear can help the phenomenon or impede it though ...

So to answer your question, @emergingsoul, you are in the soundstage and your ears and brain are guided by two primary factors—ITD (Interaural Time Difference, dominant in the midrange and bass) and ILD (Interaural Level Difference, dominant in the treble)—to perceive soundstage. ITD mainly governs dimensionality and palpability, while ILD primarily controls image focus, edge sharpness, and separation.

Much of this spatial cue information must already be present in the recording, and when it is, your system and setup/room interaction must be of sufficient quality and properly configured to preserve it. In other words, a quality system and a well-executed setup are key to avoiding the destruction or degradation of this information, allowing you to perceive a convincing soundstage.  To address your 2nd part of question/complaint...

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.