why do expensive amplifiers produce a better soundstage

The original sound is impossible to know, though. 
In my opinion, as long as your amp and speakers are adequate for the size of the room, you should be good to go.

vvvvvv6  The original sound is impossible to know, though. 

What I mean by "the original sound" is the sound of original recording played in the system. 

Ex.) Compare  Carlos269’s California Dreamin’  vs.  Original Diana Krall - California Dreamin’. 

I hear Carlos’ is closest to the original music than others below live recordings. Alex/Wavetouch audio

Diana Krall- California Dreaming in Hong Kong

Diana Krall California Dream’in

Diana Krall - California Dreaming

I think it has to do with the more expensive amplifiers ability to reproduce fine details, which are required to provide the audible cues that are required for soundstage.  Phase, timing, crosstalk, rolloff . . .  and the like all help.  Everytime I take a step up in equipment that increases details and noise reduction, the soundstage improves, but not necessarily the bass or appeal of the treble.  I agree with others though, speaker placement and the room mater the most.  

Can an amplifier interfere with sound staging? Yes. Can an amplifier create it? No, not on its own. Sound staging is all about timing and phase, so your source, speakers, and the acoustics of your room will have a much greater effect than your amp. Enjoy!

Probably a function of current output capacity.

More expensive components may help, but I don’t know why