In the recording and reproduction of bass frequencies, there is an accumulation of phase shift at low frequencies that arises whenever a high-pass filter characteristic is inserted into the signal path. It happens at the very first step, in the microphone, and then in various electronic devices that are used to attenuate unwanted rumbles in the recording environments. More is added in the mixing process, storage systems, and playback devices that simply don't respond to DC. All are in some way high-pass filtered. One of the most potent phase shifters is the analog tape recorder.
Finally, at the end of all this is the loudspeaker, which cannot respond to DC and must be limited in its downward-frequency extension. I don't know if anyone has added up all of the possible contributions, but it must be enormous. Obviously, what we hear at low frequencies is unrecognizably corrupted by phase shift. The question of the moment is, How much of this is contributed by the woofer/subwoofer, is it audible, and if so, can anything practical be done about it? Oh, yes, and if so, can we hear it through a room?
Fincham (1985) reported that the contribution of the loudspeaker alone could be heard with specially recorded music and a contrived signal, but that it was "quite subtle." The author heard this demonstration and can concur.
Craven and Gerzon (1992) stated that the phase distortion caused by the high-pass response is audible, even if the cutoff frequency is reduced to 5 Hz. They say it causes the bass to lack "tightness" and become "woolly." Phase equalization of the bass, they say, subjectively extends the effective bass response by the order of half an octave. Howard (2006) discusses this work and the abandoned product that was to come from it. There was disagreement about how audible the effect was.
Howard describes some work of his own: measurements and a casual listening test. With a custom recording of a bass guitar, having minimal inherent phase shift, he felt that there was a useful difference when the loudspeaker phase shift was compensated for. None of these exercises reported controlled, double-blind listening tests, which would have delivered a statistical perspective on what might or might not be audible and whether a preference for one condition or the other was indicated.
The upshot of all this is that even when the program material might allow for an effect to be heard, there are differences of opinion. It all assumes that the program material is pristine, which it patently is not, nor is it likely to be in the foreseeable future. It also assumes that the listening room is a neutral factor that, as Chapter 13 explains, it certainly is not. However, if it can be arranged that these other factors can be brought under control; the technology exists to solve this residual loudspeaker issue.