Is time coherence more important than dynamics: Gallo versus Green Mountain

The question I am posing is whether time coherence is more important than dynamics for long term music listening pleasure. Some background on how I arrived at this question in the course of shopping for new speakers.

In my secondary system, which is in a small room 12ft x 8ft in my Florida condo,  I substituted B & W 705 s3s for Green Mountain Chroma's which I had and enjoyed for several years. I always liked the Chromas but thought I wanted more dynamics and resolution. I planned to sell the Chroma's, but ended up taking them to my summer home where my main system is located in a larger room. (I am happy with the B&Ws, by the way.)

Spring comes and I migrate to my house in the North (nice to be a retired snowbird). I decided to upgrade the older but excellent kit speakers in my summer house and was lucky enough to be loaned a pair of Gallo Strada IIs with sub-woofer. After thorough break in I listened to them for about a week. Wonderful big sound stage, detailed, and dynamic. I was almost ready to pull the trigger when I decided to swap in the Chromas, just for fun.  To my surprise, the Chromas beat the Gallos, not with sizzle, but with a much more believable illusion of real music.  It was immediately apparent.The sound felt natural and the imaging was more precise, if not quite as big. The Chromas sounded better than they did in the small Florida room. I returned the Gallos, but kept researching to get an even better upgrade than the Green Mountains without the use of subs. I'm not sure this quest was rational, but I had the itch to approach my ideal speaker.

The real challenge is to get both the ease and natural feeling of real music with, good sound stage, full dynamics and frequency response range. After a few weeks of searching, I settled on the Legacy Audio Signature SEs. They should be delivered in a few days.

I have owned many speakers of all sorts of different design types - from Quads, to omnis, to many box speakers of various topologies.

I admit that time/phase coherence is intellectually attractive to my audiophile brain. It just seems to make sense that, if you can achieve that without sacrificing other parameters, it would be a good thing.

Plus, I’ve had a long love affair with Thiel speakers which have always sounded a bit special to me in certain respects: a certain tonal correctness and an image focus and density that gives the impression all the energy related to any instrument or voice in the mix is being lined up correctly for maximum solidity and palpability. Many other speakers afterwards tend to sound sort of diffuse to me, even ones that image well.

So it’s very tempting for me to just go ahead and ascribe these attributes to the fact the Thiels are time/phase coherent. (Dunlavy speakers also seemed to have these attributes).

On the other hand: I’ve also had time/phase coherent speakers - e.g. Meadowlark - that had some of those attributes but not all. They did not have the image focus and density of the Thiels, and sounded a bit less neutral.

My Quad ESL 63s were also time/phase coherent (as I remember) and did not have have the focus and density of the Thiels either. 

Also, I’ve had and heard really astonishingly beautiful and believable tonality from speakers using the usual steeper crossovers and no time/phase coherence.  (Love my MBLs!  And Hales and Waveform and Spendor speakers....)

So as much as it’s tempting, I’m not confident about leaping to the conclusion time/phase coherence is necessary for very realistic presentation, or that it is for sure responsible for what I like about the Thiels.
I based my original question on my home trial of the Gallo Strada lls and the Green Mountain Chromas which I compared for over a week. In my shopping experience I did audition Vandersteens, known for a time coherent design. They also sounded very natural to me. It may well be that time coherence is sufficient for this natural sound quality but not necessary.

 As has been said these qualites are probably not mutually exclusive even though they seem to me to often not be found in the same speaker.  In an effort to experiment, I put Seas Melenium Tweeter in the Chromas today. (I had them in my kit speakers) They sounded livelyer and more resolving. Maybe you can get both vivid dynamics and naturalness as in live music.
Isn’t phase response dependent on seating location and room? I would think that DSP adjusted phase correction such as with Dirac Live would be the ideal solution to fixing this issue? Then you can just focus on getting the most dynamic speakers you can.
The effect of advanced DSP on correcting speaker drivers that that are not quite mechanically in phase or time aligned is a question that is above my pay grade. Very interesting. This could be the solution.