@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.