Is soundstage width a myth?

It is an illusion, but one that is made better by good room acoustics.  Diffusion between and behind the speakers and listening chair can be the missing link.

I always wondered why people don't just buy 4 speakers for an amp that would separate the vocals and instruments. Possibly a stupid idea, but similar to the purpose of the subs?

Yes/no/maybe

EBM excellent answer.

     Whenever imaging or soundstage are mentioned, I like to remind people about these resources: The following provide tests, with which one may determine whether their system actually images, or reproduces a soundstage, as recorded. 

      ie: On the Chesky sampler/test CD; David explains in detail, his position on the stage and distance from the mics, as he strikes a tambourine(Depth Test).

     LEDR test tells what to expect, if your system performs well, before each segment. 

    Chesky CD contains a number of tests, in addition to the LEDR.

 (https://www.audiocheck.net/audiotests_ledr.php) 

 and (https://www.amazon.com/Chesky-Records-Sampler-Audiophile-Compact/dp/B000003GF3)

     The shape of your ears’ pinnae is also a variable, regarding your ability to perceive images/locate sounds.

     A Stereophile article, that explains the LEDR test: http://www.stereophile.com/features/772/