Good post andy!
I don't feel competent to assess the exact contributions of phase/time coherence to what I hear with the Thiels. And speaker designers (and experts on acoustics from what I can tell) still seem to disagree.
I can only note that my Thiels (first CS6, then CS3.7 and 2.7) share a quality of precision in imaging, a solidity and density of imaging, and a very believable natural tone for voices and instruments.
Also, the 3.7s/2.7s are the most coherent dynamic speakers I've heard. The 3.7s in particular all the way through the bass region. But both designs distinguish themselves in coherence in the mids and highs. There is simply no sense of a "tweeter" in the sound from the mids. Zero. Sounds that traverse the tricky crossover points of the tweeter/mid driver sound perfectly whole and coherent.
What gets interesting to me, as a nut about instrumental/vocal timbre, are how different approaches can still seem to do well. I remember the very well regarded speaker designer, Paul Hales, saying that one reason he chose higher order crossovers instead of chasing time/phase coherence is that he felt the benefits of higher order made it easier to achieve timbral precision. And to my ears Hales speakers, the Transcendence line in particular, excelled in exactly that aspect.
I remember going to a CES way back and after having been in most rooms over two days I heard what sounded startlingly like a live band coming from one room. It was the Hales room and I'll be darned if the timbre of the horns, saxes and other instruments coming through those speakers wasn't astonishingly rich, accurate and believable. When I ended up with Hales transcendence speakers, this was their prime virtue (though I found ultimately they suffered a bit from a lack of dynamics/palpability, which the Thiels really give me).
My current favourite speaker for accurate-sounding timbral quality are the Joseph speakers. I played a great many recordings on those speakers that I've played for years on my Thiel speakers. I love, love, love the sound of the Thiels, but when I played for instance certain piano recordings on the Josephs, there was a hair-raising shock, the sensation of hearing a piano's timbral quality *exactly* as I'm used to when I play one, reproduced right in front of me.
So these encounters with auditioning and owning various speakers that at the very least seem to give the Thiels a run for the money in the timbral-accuracy department, make me hesitate to conclude the only way to get such things "right" is time and phase coherence, as intuitive as the case for time/phase coherence may be.
(Please don't throw tomatoes at me my Thiel brethren, I'm still one of you!)