I understand what I said there. But clearly you don't. Differential in arrival time between your ears is what is audible (you can tell the location of the sound this way). That has nothing to do with the phase shift upstream in your system. Clearly you have not watched or understood that video to make comments like this. In Music reproduction, this differential is provided by what comes out of each speaker with respect to volume and timing which is content dependent for the most part.
There are a few ways how phase shift can be noticed, it usually involves multitone waveforms that are partially phase shifted (again phase shift and delay/anticipation per frequency is equivalent). These topics are still "differential" as in reference to somewhere in the waveform, which is kind of the point. However, it is not in the sense of left and right ear.
- Subwoofer placement usually needs phase alignment, so does the integration of speaker drivers
- Another obvious one is that one can take a frequency band and delay it by an arbitrary amount. The signals still have the same 'local' RMS and for pure sine waves, nobody would notice (this is the limit of frequency analysis, it requires "steady-state" but it is of course useful because everything else is way more complicated). However, music is aperiodic and we notice delays, e.g. if the singer or beat runs behind/ahead of the rest.
Unrelated, we usually want a signal "true to the source", i.e. hifi, no?
