why do expensive amplifiers produce a better soundstage

It has been my experience that a great tube preamp does help foster soundstage. Since the preamp must mate well with the amp they both can play a role. 

Price means nothing. Low noise floor & crosstalk between channels. 

Emphasis or lack of emphasis on one frequency or another can alter the perception of the "stage"

My subjective opinion on my personal experiences is that tubes alter this perception to a higher degree than the S.S. components I have used. Tube rectification vs diodes when trying both in the same type preamp circuit has an affect/effect? as well. I favor tube rectification in preamps. 

Ultimately the recording & speakers/room set up hold the biggest key to stage perceptions. All of my comments are solely based on my opinions 

@roxy54 

The Merman’s are of my own design based on used parts. Total investment was ~$1,500.

ORIGIN

I was dis-satisfied with the way the L300s rendered female voices (especially Joni Mitchell) and was determined to produce a speaker that could do females justice. But the caveat was that they had to play LOUD! Ethel Merman was well known for having a very powerful voice, but being Too Loud "Too loud they said," she says in one of her movies.

Ethel Merman (born Ethel Agnes Zimmermann, January 16, 1908 – February 15, 1984) was an American actress, artist, and singer.[1] Known primarily for her distinctive, powerful voice and leading roles in musical theatre, she has been called "the undisputed First Lady of the musical comedy stage".[2]

Among the many standards introduced by Merman in Broadway musicals are "I Got Rhythm" (from Girl Crazy); "Everything’s Coming Up Roses", "Some People", and "Rose’s Turn" (from Gypsy—Merman starred as Rose in the original 1959 Broadway production); and the Cole Porter songs "It’s De-Lovely" (from Red, Hot and Blue), "Friendship" (from DuBarry Was a Lady), and "I Get a Kick Out of You", "You’re the Top", and "Anything Goes" (from Anything Goes). The Irving Berlin song "There’s No Business Like Show Business", written for the musical Annie Get Your Gun, became Merman’s signature song.

Performance style
Merman was known for her powerful, belting mezzo-soprano voice and precise enunciation and pitch.[40] Because stage singers performed without microphones when Merman began singing professionally, she had a great advantage, despite never taking singing lessons. Broadway lore holds that George Gershwin advised her never to take a singing lesson after she opened in his Girl Crazy.[41]

Profanity
Merman was notorious for her brash demeanour and for telling vulgar stories at public parties. For instance, she once shouted a dirty joke across the room at José Ferrer during a formal reception.[54]

While rehearsing a guest appearance on The Loretta Young Show, Merman exclaimed "Where the hell does this go?" Young, who was a devout Catholic, advanced towards her waving an empty coffee can, saying "Come on Ethel. You know my rules. That’ll cost you a dollar." To which Merman replied "Ah, honey, how much will it cost me to tell you to go **** yourself?"[55]

This is where the magic happens.  The 0.68 Clarity cap will be replaced by a 0.52 mfd Sprague polyester to add detail without as much edge.  The AMT has been treated with my own special modifications rendering a completely different sound with tons of detail.

https://youtu.be/OmWNOi6b4ak

@toddalin 

I'm almost sorry I asked. I'm well aware of who Ethel merman was, but it would have been more interesting to know what your speakers were composed of.

@roxy54 

JBL 2241H 18", JBL 2251J 10", ESS Heil AMT.

I purchased the 18s in the JBL "clone" cabinets from a local church.  I purchased the 10s from eBay as well as the Heils (from a 1D) that included cabinets and woofers.  Luckily, for shipping, the 10s were close and the Heils/cabinets were local.

I made the wooden cabinets for the 10s as well as the acrylic stands and horn flares for the Heils using laser cutting and 3D printing.  I also 3D printed the ports for the 18s.

The real secret to the Heils!

https://audiokarma.org/forums/threads/im-fixing-a-hole-heil.1025205/