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

@holmz , you can be snarky all you want as long as you are right. If I posed as a Buddhist everyone would die laughing.

Although timing errors can affect imaging frequency response variance between channels causes much more damage and that is easy to demonstrate.

As long as DSP has control over individual drivers it can perfectly adjust timing in one listening location. Most multiway speakers do not allow for this. They have to be bi or tri amped. However, time alignment is most important for subwoofers as diminished transient response affects impact. Fortunately, subs are amplified separately. DSP was extremely effective 25 years ago with the advent of Radomir Bozevic's TacT Audio. He wrote the book on "room Control." With the faster processors we have today it is even better due to increased bit depth. My solution to the problem since 1979 was to use one way loudspeakers with subwoofers. There was no easy way to time align subs until the mid 90s with TacT's processors. Today the best are probably Trinnov's units. But inexpensive and effective ones are available from MiniDSP and DEQX. Used correctly they can improve almost any systems performance even the ones owned by digitally phobic people. It is all just lay instinct. 

Rooms certainly are "Time" sensitive. Reflections occur in time and their timing determines how we will hear them. Unless you like listening to bands in a closet early reflections are always bad. People say that late reflections are in part a benefit and one should not get rid of all of them or the room will sound "dead." I am not so sure about that. Timed reflections are in the recording giving you a sense of the size of the venue the recording was made in. Studio recordings frequently have fake late reflections added (reverb). The problem for home reproduction is that these sounds do not come from the right direction. I am beginning to think that in most home situations there are no late reflections only strong vs weak early reflections. If the room is big enough you get echo which is peculiar to that room and only pollutes the music with sounds that are not supposed to be there. 

@jeffvegas , I will do it for you. One way, 8 foot ESLs are King.

As I said earlier in this thread, I have compared 2 speakers, one set time aligned, the other set, not.

They are Jeff Bagby's DIY kits, the "Kairos" speakers, and his "Adelphos". Same drivers (the great SB Acoustics 'Sartori' ring radiator tweeter and 6' MID), same size enclosures. The Kairos are aligned, the Adelphos were designed for those who don't want to tackle building an angled enclosure. 

As good as the Adelphos are, the Kairos created a bigger soundstage and more precise image. 

@mijostyn I would like to be a Buddhist, but that is about as far as I got. But I do know enough to know that snarkiness is not a positive attribute.

I am pretty sure that the phase is usually more critical with bass than timing.

Our ears and brains are good at getting the direct path, and depending on the speakers directivity and echoyness of the walls, then reflections usually affect the frequency response.
The more delayed echos, can add some ambiance.

I agree it gets complicated in a room.

@holmz , phase and time are attached at the elbows. It is certain easy hear what happens to imaging if you compare the two channels 180 degrees out of phase. The smaller the phase angle the harder it is to hear. Time, when you are talking about a few milliseconds or less with subwoofers is audible if you cross where I do up at 100 Hz. Lower down it is something you feel. As time variation increases the transient response of the bass has the edge taken off and you do not feel the impact as abruptly. Go to a small jazz club.  Listen and feel the bass drum. That is what you are shooting for. Time aligning subwoofers empirically is a real PITA. With a measurement mic you can do easily and know that you have it right on. The advantage of DSP here is that you can keep the subs where they perform best and align but delaying the signal of which ever speakers are early. 

As for room acoustics I have come the realization that too much absorption is better than too little. The acoustics of the venue are either in the recording or are being created with echo. There are not many instances where we listen to music in small rooms. You really want to minimize all early reflections but in a small room they are all early until they bounce around several times. Speakers that have sharp dispersion limits such as horns, planar speakers and linear arrays have large advantages acoustically in residential rooms. A properly deadened  small room say 16 X 30 sounds better than a really big room with high ceilings because these rooms usually have acoustic signatures that are harder to get rid of, they echo.

Reflections certainly change frequency response which can be easily seen with a measurement mic. But, they also smear detail and ruin the image.