Restock, I appreciate your intellectual curiosity about this issue, but it strikes me that you are asking but not accepting the sharing of experiences you are receiving. I can tell you only what my ears tell me while listening to my system.
Doug Deacon's experience matches my own exactly. We approach our solutions to this somewhat differently, but we we share the same experience, we are hearing the same things, and we both adjust VTA on an LP-by-LP basis. In my case, I have settings marked that are ballpark correct for "most" 120 and 180 gram records, and which I have carefully selected based on the interplay of VTA and VTF on my tonearm (each affects the other). I start at that applicable ballpark setting for the given LP (or slightly off from it if the record is 150 gram or 200 gram, based on experience). I then will adjust by ear if things are not sounding right: if it doesn't sound dialed-in, I simply stop the record, make a VTA adjustment, and start up again. My tonearm allows for very minor adjustments (in the .001" range and continuously adjustable), and even very small changes in this sub-.005" range can, on some LPs, make a difference in whether everything locks into place or not. I have experienced the sonic improvements such minor adjustments can make, my listening partner spouse has experienced it, my audio friends listening on my system have experienced it, and the manufacturer of my turntable experiences it. We've done it numerous times in our listening sessions together.
I try not to get compulsive about VTA - after all, this is about enjoying the music! - but I do pay attention to it and often I notice that when I'm simply not as engaged in the music, often the VTA is slightly off.
I will also add that, in my system, the answer to why such minor VTA changes are audible is not an artifact of mechanical stability variables as you hypothesized could be the case. My tonearm (Walker Proscenium) is not adjustable on the fly for exactly those types of concerns. Locking rings and a set screw bring the toneam to a mechanically rigid state after adjustment, and must be loosened to make any adjustment; nevertheless, it only takes 10 seconds to make an adjustment.
Your question, however, was is such extreme accuracy "NECESSARY." My answer to that specific question is: in my system, yes, it truly makes a difference and I hear it. I don't always bother with it and still enjoy the music, but to get the maximum quality of playback that the system can deliver, it is absolutely necessary to pay attention at these minute degrees of difference. And, I don't always do it because sometimes I'm not being that pickly; sometimes FM radio is OK, but most times I'm looking for more - especially in my listening room.
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Speaking of which, I've just come back to edit my post to share this experience after writing the above: As I was finishing the post, I was being troubled by the piano reproduction on a Philips LP of the Beethoven Cello Sonatas with Rostropovich and Richter that was playing as I was writing (Philips 835 182/83). The piano sound was "shattering" slightly on some strongly struck notes in some louder passages at the end of the last movement. I changed the VTA by possibly .002" (two-thousandths of an inch), relocked the arm and replayed the section. The "shattering' was gone and the notes were reproduced in their full clarity and dynamic.
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