I agree, the record needs to be corrected.
Clearly it has been shown that it is possible to create an example of audible phase shift. The question is does the normal level of phase shift found in a Hi-Fi audio system rise to the level of audibility? The only time I have "clearly" (reliably able to ABX) heard phase shift differences is when I made a mistake with DSP trying to correct phase and really screwed things up.
I have my own anecdote. I was aware of this thread and that experts think phase shift is inaudible. So one day a few months back, I decided to do a really ham fisted phase correction on my linear phase system. The verification measurement was the same as the control, except for the phase response which was commendably flat. So I sat down to have a listen. I was quite shocked to hear the soundstage had lifted up off the floor and the whole thing was vertically compressed, as if I was listening out of a letter box. It was not subtle at all, in fact it was quite horrible. I did not blind test, but I am pretty certain I could pick it 10 out of 10.
This lead me to months of investigation where I made and re-made filters with a lot of verification measurements. That made me realise that beyond a certain threshold, phase is indeed audible and if you deliberately throw out the rules of DSP and do something you shouldn't, awful results will follow. So the question now is, what is the threshold for audibility, and is there any point in pushing the correction further? Should we be content with phase distortion produced by all passive crossovers, all speakers with IIR DSP's, and in fact nearly every minimum phase speaker on the planet?
The new version of Acourate has a procedure for linearising the phase of each individual driver. I have to admit that I have some concerns about this, especially since I am taking the measurement from 1m away.
@NTK has pointed out in another thread that in the nearfield, pressure and particle velocity are out of phase. So I may be taking an unreliable measurement, and therefore performing an unreliable correction. But I can report that it actually sounds quite good.
My own experiments suggest that there is indeed an advantage in going linear phase, but I am not going to convince anyone without evidence.