I think I do understand what you mean, but it also seems to me that different people use the term very differently, and to mean subtly different things... to me the term "over-analytical" seems more accurate to describe "the condition" you're talking about. I agree with you that something that over-emphasizes the separation between individual elements is not a good thing, however I don't see that as being part of the same "scale" between accurate and not accurate. In other words, to me, being analytical means "being totally uncolored and accurate and not covering anything up" - and exaggerating the differences goes past "being totally analytical" and into something else - being inaccurate in the other direction altogether.
I prefer to use the analogy of a picture. When you take a digital photo, it can be sharp or blurry, and the color can be accurate or not, and the contrast and brightness can be accurate or not. These are all things that can be measured, and each can be more or less accurate, but I would say that "being analytical" or "being accurate" means that all of them would be "correct". Now, it may be that, from an artistic point of view, we may prefer a particular photo if it is less accurate (for example, it's common to deliberately blur photos of faces to hide blemishes, and to airbrush entire bodies to de-emphasize obvious flaws, and deliberately exaggerating colors looks very cool in certain cases). However, very few people I know would deliberately buy a blurry TV so old movies look less obviously bad, or deliberately buy a poor quality camera because it doesn't show up the flaws in their subjects. (Many photographers use a "gel" filter to "soften" certain pictures, or use equivalent post-processing in Photoshop, but very few would buy a camera that was incapable of delivering a sharp picture if called upon to do so. Likewise, you might consider a TV that includes a "soft picture" option for watching old movies, but probably only if it has an "off switch" for when you don't want it.)
Now, Photoshop also has an option that allows you to "sharpen" a picture after it is taken. In reality, what this feature actually does is to boost the contrast ratio around edges. (Processing a picture to deliberately add slight halos around high-contrast edges - a dark halo on the dark on the dark edge and a light halo on in the light edge - makes it appear to be sharper.) However, it's really a sort of optical illusion. It doesn't actually add detail but, by making the details that are already there more apparent, it makes the picture seem more detailed. If properly applied, this trick can make a too-soft picture look very good, but, if over-applied, it produces an exaggerated effect that looks unnatural. To me, the way a picture that's been over-sharpened looks is exactly analogous to the way some equipment sounds - and like what you described - almost like someone has artificially outlined the edges of each instrument or note (and this seems to be what some people describe as sounding "etched" - which is a great description of how over-sharpened pictures look).
My point of that somewhat long winded description was to demonstrate that the two "directions" are NOT really a continuum. Even though it may seem that way to people who've never taken a picture or used Photoshop, there isn't a single "control" that goes from "blurry" to "sharp". There are really two separate controls, one for "added blurriness" and another for "added sharpness". And, to me, if applied to a picture, the term "analytical" would mean - NO added blurriness and NO added sharpness. (No-one would describe the cartoon-like picture you would get if you turned the sharpness all the way up in Photoshop as "analytical" - they would describe it as having exaggerated sharpness - or even as looking like a caricature.) You can add "blur" to compensate for a certain picture being "annoyingly sharp", or to cover up details you'd prefer not to see, and you can add "sharpening" to compensate for a picture that's "too soft", but they are still two distinct colorations, and the the most accurate picture will have none of either (and, with images, there is a pretty obvious point where that is true).
I believe that a lot of audiophiles don't understand this distinction... and to me it seems pretty important. If your headphones and amp blur the details, then the solution is to reduce the problem that causes the blurring, but that's not the same as taking something that's neutral to begin with and add something that artificially boosts the "audio contrast". You can't make the blur go away by adding sharpness - at best you can create an illusion that makes it look superficially better. And, likewise, if something alters the sound in the way you describe, which I would equate to over-sharpening a picture, then the solution is to reduce the flaw that's causing the error in that direction, but that's not the same as simply "adding blur". But you DON'T fix an over-sharpened picture by adding blur. (You might argue that adding sharpening to a blurred picture does in fact improve it, but most photographers would agree that doing so is a last resort, only used after you've done your best to eliminate the original error.)
To me, from a technical perspective, it seem like an awful lot of discussions about headphones and amps come down to "this headphone is too sharp - I need to find a blurry amp to go with it", or the reverse, as if there were in fact a single control that went from one to the other. (To me, this seems rather like trying to correct nuances in frequency response with one of those old "Tone" controls, rather than using more accurate Bass and treble controls... and I can't imagine an audiophile using a Tone control to correct for his overly-bright speakers - because it's obvious that the solution almost certainly won't "line up" with the problem. (If we're talking about a simple aberration in frequency response, then boosting the treble in one device to compensate for a roll off in another may produce a good result, but that's usually NOT what we're talking about, which makes a proper and effective solution somewhat more complicated.) If you agree with my assessment, then it also becomes obvious that we must differentiate between correcting a problem where a device is adding unnatural and excessive detail, and starting with something that's simply totally accurate, then reducing the amount of detail because of a personal preference for a softer audio picture, or because we're listening to flawed source material which simply sounds better when we don't hear all the details.
Personally, I much prefer to do my best to start out with "perfectly neutral", removing as many colorations and imperfections as possible, then adding the precise colorations and alterations I like, rather than to try and find more or less random combinations of flaws and colorations that add and cancel in such a way that I like the result. (Both because it seems like "the more rational way to do things", and because that way I don't have to re-think my entire system every time I "throw off the delicate balance" by changing one component or another.)
(That's why, to me, saying "over analytical" is sort of like saying that a picture is "too perfect".... in that it sort of doesn't make sense .... To me, a "perfectly analytical" system would make it so each individual instrument, and even each note, was precisely distinct and not at all burred together but, at the same time, wouldn't exaggerate the separation between them either. Anything past that would have crossed from "analytical" to something else... )
