I haven't built anything so I'm not really sure if this is addressing the same issue of phase as applied to the discussion but Floyd Toole in his
summary of research at the NRC into loudspeaker performance that is described in two classic 1986 papers [32, 33], concluded thusly: "The advocates of accurate waveform reproduction, implying both accurate amplitude and phase responses, are in a particularly awkward situation. In spite of the considerable engineering appeal of this concept, practical tests have yielded little evidence of listener sensitivity to this factor...the limited results lend support for the popular view that the effects of phase are clearly subordinate to amplitude response."