a few points
flat frequency response is easily obtainable in front of speakers but if the idea is to make a loudspeaker sound good, truly flat frequency response is the wrong goal (google ’bbc dip’)
time coherence is only meaningful if delivered at the listener’s ears, which is not so easy in a domestic listening environment
phase response/inversion has rarely made a major difference in the sound in my own experience (many hifi units allow for remote switching of phase, so it can be very easy to test for oneself)
lots of the things about speakers and what makes them sound good are hard to measure, so as in many things in hifi audio, measurement based criteria are necessary but insufficient conditions for a pleasing result