Tonal accuracy is very important, but how does one know what “accurate” means in terms of the soundstage characteristics noted above? If you mean accuracy in terms of spacial localization precision, I will say that the Omnis may not match others. The AMT dioples do better than the omnis on this, as good as the box speakers in my early comparisons.
Relying on Griesinger papers, sound is more accurate with stream separation, and less accurate without, due to auditory system, your internal processor! This doesn't mean anything absolute, it just means that if you find what you perceive is not accurate, first make sure you are having stream separation going on by finding where the transition is and then moving closer to speakers than that. If it's still not accurate, you can logically reason it's the recording, or something in your setup as it is not your auditory system. No matter what the state of recording or playback system, you have it now more accurate than further away anyway! Point is, you now know it's not your auditory system that makes it less accurate, but something else, there is no confusion and logic can be applied.
Not knowing your auditory system affects, you might grave for more clarity for example, go and buy new speakers or amplifier in order to improve clarity only to notice it's still not there what you heard on the shop floor. You could have had stream separation happening in the hifi shop as it's different acoustic environment and likely optimized for good sound and mistakenly think it is the amplifier you are listening to, when in reality its your own auditory system giving more everything, paying attention! Then get the gear home, and have no stream separation and so on as you are not aware of any of this, might perceive no clarity and be disappointed to the purchase. While the problem could have been simply your auditory system not being able to provide clarity all along. Another, go buy cables, swap them in and go take a good listen and just to make sure unknowingly lean forward to hear better, and sure enough hear a better sound! and conclude, Yes, cables matter! Except they likely sound exactly the same as previous cable, you just made stream separation by leaning forward and perceive a change without ever knowing it.
Importance is being aware that auditory system matters and affects what you perceive regardless of gear and room, it's always with you. Learning to listen your own auditory system makes it possible to reduce confusion about what you hear, and instead enable use of logic.
Clarity, tonal accuracy, timbre and such are critical aspects of “good” as much (more?) than soundstage aspects of size, spatial precision, and “envelopment”. I did notice a lbetter clarity when moving closer to the BMR box speakers, but can’t quite figure out why that was not so with the AMT dipoles.
Yes, everything matters and at least some of it is not mutually exclusive, for example tonal accuracy could be off in absolute terms, but as long as both speakers match you could still have strong phantom image and make the "clarity" of your auditory system happen. Or, even if tonal accuracy was spot on, you might not have (max) clarity if your auditory system doesn't have stream separation going on.
If you find two speakers differ be aware that polar pattern and edge diffraction could make sound tonality vary a lot with listening axis, here is why you'd want good smooth polar response and optimize edge diffraction: sound would stay tonally correct no matter toe-in, and toe-in could then be utilized just to optimize spatial quality of (room) sound. If polar response is bad due to what ever reason, there is about one good listening axis where the toe-in must be locked, spatial quality cannot be adjusted otherwise you'd compromise the tonality.
Auditory system is separate adjustment layer basically, your speakers and room could be anything, ideal, yours, mine, and you could still change the sound by changing listening position as your auditory system locks in or not, stream separation or not. This is why I think auditory system as a subconscious thing in a way, it determines what I actually perceive with my conscious mind, it is like a filter layer between ears and mind. In general the speakers, room and positioning should be adjusted so that the filter (auditory system) gets into a state which provides sound you want to hear with your conscious mind, the one you logically think about the sound, the one you listen with. Auditory system is always there doing it's thing and you cannot swap it to another like speakers, or manipulate directly like EQ knob, but you could learn how it works and affects perception, and then indirectly exploit it to your advantage by adjusting positioning for example.