I think the “problem” of this theory would be that the scales existed before ths chords and that the elements of a triad (the chord of thirds) have been considered for centuries as dissonant.
So a theory of fill-in tones would bridle the horse on the tail. The most reasonal explanation to me would be the description and treating of sustained tones, passing tones and changing notes as elements in the chord theorie and the phenomen of chromatic approaches. But in history of music this period has been too short between early baroque and the concept of 12 tone music.
I have never heard about something similar and don’t remember a treatise of chords were the 2nd, 6th or 7th have been introduced in another way than in the mentioned above or as additional tones in a tower of thirds.
(Except of Debussy’s scales of foreign countries like Bali and Java there are still other scales like the whole tone scale and the scales of 12 tone music that wouldn’t fit in this theory.)
I just went through your link chord of nature. Well, I‘ve fully ignored the overthone serie!
So I‘d like to add: another problem would be that in history of music everything that had been practiced for some generations was later (by the following generations ) considered as given by nature ... and not only in music theory!