why do expensive amplifiers produce a better soundstage

Surely, those expensive produce a better soundstage. However, this is not. 

The DIYer's do have passion in building the super amp with top notch performance. 

Adequate power to negate frequency shifts due to speaker impedance variations.  This doesn’t necessarily require that the amplifier be expensive but some things to look for are a robust and quiet power supply, adequate power for the sensitivity of the speakers being driven, and the ability to nearly double power into lower impedances, which is more critical when used with hard to drive speakers.

OP  expensive amplifiers produce a better soundstage

You should be aware that the soundstage here is only in the electronic unnatural sound world term. It’s not the same music we hear from recording studios or concerts. It’s a purely imaginary sound art. To non-a’philes, it’s just ear-hurting distortion noise veiling the real music. Alex/Wavetouch audio

OP

In my Opinion, soundstage is not really a relationship of Cost of an amplifier

as others has posted and their thoughts, for Me, it is about the ROOM and the system synergy. I was on this quest for a few years and really wanted it . I had to compromise as my room is a bit small / medium. I was able to attain what I was looking for. 

Yes, my gear is a little bit more $$ but that soundstage will disappear if not for the room tuning and synergy that i was lucky to chance upon. I have heard music from amps more money than mine that has a bigger soundstage and In retrospect, I also heard amps that more $$$ than mine and has NO soundstage.

in the end, as i stated, it about synergy and the ROOM

To non-a’philes, it’s just ear-hurting distortion noise veiling the real music. 

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

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. With these spatial cues, they can easily distinguish whether the images are clear or veiled. To them—that is, to non-audiophiles—these attributes are not distortions.

Spatial cue information can be recorded, mixed, and produced in a way that is sometimes even better than what one hears in person in a studio or live concert when proper close multi-miking equipment and techniques are used on individual instruments. Some people, including myself, actually enjoy this because it can restore spatial cue information that would otherwise be lost in a poor acoustic listening environment.

Imagine yourself sitting in two different concert halls listening to the same symphony orchestra. One hall has better acoustics than the other and therefore delivers a superior listening experience. Proper recording, mixing equipment, and techniques can minimize the negative effects of poor room acoustics and help restore optimal sound quality. Most award-winning engineering recordings are produced using multi-miking techniques.