Does Time alignment and Phase coherency make for a better loudspeaker?

One of dozens of variables that can be used to build good speaker... undoubtedly doing this has a negative effect on something else. Audio design is all about trade offs.

Well said. I think with the improvement in driver technology and materials the compromises of 1st-order crossovers has been largely mitigated, but there are always trade-offs. I had Thiel CS1.6es in my system for a while, and I do think there is a certain “rightness” about a well-implemented time/phase coherent design, but that said I hear a lot of the same properties from the likes of Joseph Audio so pick your flavor. All else being equal, which is NEVER the case, I’d take time and phase coherency, but only IF the rest of the sound profile meets with my overall tastes.

OP

Caps lock key broken?

Angeling the speakers back reduces 1st reflection problems, ....it isn't time aligned

Listen for yourself.

I'm afraid that while much is made of it, I've heard time aligned and non time aligned systems and... MEH!

For me it's not the convincing superioiur sound experience the vendor's claim, and acousticians I trust say the same.

That's not to say there are not some very excellent time aligned speakers.  The top of the line Vandersteen come to mind.

Certainly it makes for better sound staging and imaging.

...however, there are varying degrees of what the industry describes, for example, as "time alignment" out there. It can sometimes strike me as more of just a marketing thing...as though either the makers think that at least half the buyers don't really understand what a proper time alignment can attain...or that half the makers don't understand it...or both maybe, IDK. 

Everybody has their own way of making and selling speakers, or choosing them FTM. But IME when you technically do this topic justice, you do get some pretty good rewards.