It appears I forgot to answer why I insist on submitting polyphonic tabs using Hookpad 1.8 instead of the “draft” version which takes away the extra voices and the mixer settings.
Sometimes the countermelody is of equal, or even greater importance to the melody. This can happen if for example there is little or no accompaniment; the countermelody provides the harmonic context more than Hookpad’s invented chord track does. Take the instrumental section of this tab for instance. Towards the end is a chromatic descent using several non-trivial chords. Why aren’t they a constant sequence of dominant seventh chords? Why do the inverted minor chords show up there? It is because the first measure repeats itself a minor third lower in the next measure. The iii6 chord locally behaves like a Phrygian cadence, while the i6 brings the song back to the home key. This information would be unavailable without the countermelody track.
Other times, it is simply because the countermelody is easy to transcribe, and adds extra color to the analysis. Not just classical music, but early video game music also has few voices without other accompaniment (including the instrumental section above). In these cases, only the melody, countermelody, and bass are present in the original song; if the countermelody track were muted, the remaining voices would sound empty and have trouble forming chords on their own.
More recently, I have been interested in how human voices structure harmony in contemporary music. They are expected to fit inside a pitch range smaller than many musical instruments, because this helps listeners remember the melodies and reduces strain on the singers themselves too. The supplementary voices may go below, above the melody, in both ways, or stretch across multiple notes; I think this tab illustrate those possibilities nicely. The countermelody may even cross the melody, such as in this tab. Instead of being always spaced a third or a fourth against the melody, they could also reinforce the song’s harmony, like the chorus here: small details that explain how the voices “resonate” with the music. And when you have enough voices, they can overlap in a myriad of ways, like this or the OP’s Wonderful Stories example. They are an integral part to popular music, which the Hooktheory books focus on, and definitely worth studying or analyzing.
Hookpad is unique among not just music theory analysis tools but DAWs in general, in that it provides a diatonic piano roll editor. This makes intervallic relations between interdependent voices more prominent than a chromatic piano roll could achieve. The best way to take advantage of that is to permit the use of such intervals in the first place; in fact, if the Hooktheory books are to ever touch on multi-part writing, it is hard to imagine Hookpad still locking the extra tracks away from the readers of the book. The main reason I submit those polyphonic tabs, therefore, is to reinforce the view that these extra voice tracks do play an important role in harmonic analysis.