Can anybody provide a technical reason that a solid state amplifier topology would have any effect on the sound stage? I am unclear as to what exactly is the cause of this reported design limitation/flaw.
I can't. I can only say that during my long/happy association w/tube amps & preamps, I consistently noticed certain qualities of all-tube designs that either didn't exist in SS, or existed in truncated form:
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Soundstaging was notably different with tubes. Typically both tubes & SS did soundstage width well, but only tubes gave that greater depth of image placement, both in front of & behind speakers
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Tonality was also notably different with tubes. Some tube designs had slight upper midrange "glare," it tended to be rather friendly sounding, rather than overtly bright. By contrast, many SS designs had boosted upper midrange and treble, and often this was perceived as overt brightness.
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Bass (deserves its own section): tubes sometimes had relatively deficient bass, but not always. Some tube designs went deep. But SS designs routinely has greater bass extension as well as obviously better damping (how quickly bass notes start & stop). The other big difference concerned a quality of the tube bass some term "wet," while others call it "rounded." I did hear that, and it generally sounded better than the somewhat dry quality of SS bass. The very best tube amps go low and sound relatively flat (not extremely wet or rounded); while the very best SS designs tend to have more real-sounding, fuller bass.
-- Verismilitude: fancy word that means having the appearance of reality. Not sure how to say this, but despite their at times inferior specifications, many tube designs simply sounded more "real," with notes billowing into audibility, then decaying, as they do IRL. The timbre of each instrument (ie, clarinet, violin, bassoon) was far more evident w/tubes.
I have yet to hear any of this on the desktop, or with headphones. My tactic instead has been to get several "endgame" SS amps/preamps that explore things like soundstaging and space around notes in exemplary SS ways--and let me use balanced/XLR out for headphones, something you very rarely see w/tubes.