Cerrot ... your comments, from an aspirational perspective, are valid. But aspirations do not necessarily align with reality. I suggest that you read the many posts in the "Sloped Baffle" thread. In particular, read Roy Johnson's many posts about 1st order cross overs and using sloped baffles. I recall that Bombaywalla and a few other similar thinking folks have also posted some very insightful comments.
Just an fyi, most speakers that use passive cross-overs are NOT time coherent, even if they are phase coherent at their respective x-over points. The physics is explained in the "Sloped Baffle" thread. Roy Johnson's White Papers are excellent resources as well.
To my knowledge, there are only 3 conventional driver speakers on the market that purport to be time and phase coherent; namely Vandersteen, Thiel and Green Mountain Audio. There may be others but I don't know which brands they might be.
The 3 brands mentioned above share several common design parameters. One -- first order crossovers (roll-off is at a 6db per octave slope); two -- sloped front baffles to mechanically align the voice coils of the various drivers; and; three -- drivers that operate over a wider pass band as compared to more conventional drivers.
In the case of the 3rd point in the preceding paragraph, drivers cross that over to each using a 1st order cross-over necessarily must operate over a wider pass band. By comparison, my Paradigm's use 3rd order crossovers between the mid and tweeter drivers. I believe that equates to a 24 db roll off rate. In short, each driver's operational pass band is much tighter.
While time coherent design features provide obvious advantages, they present design challenges as well. For example, drivers that operate over a wider pass band tend to be less linear. Also, their output may become congested at high SPLs and or when playing complicated musical passages.
My point is that there is no magical solution that solves every design parameter perfectly. So, be it going the Vandy, Thiel or GMA route, or using a DEQX with a more "conventional" speakers, or just living with time incoherence, ... there are trade-offs.
Welcome to our hobby.