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.