Also a lifelong musician here, and I think you're completely wrong about harmony. Western music (assuming that's what we're talking about here) IS directly derived from harmonic progression. It is truly the core of the music. The underlying chords are the obvious harmonic progression. Melody is just an expression of underlying harmonic structure. Rhythm is meant to emphasize the changes and movement of harmonic structure. Timbre itself is meaningless without a note to carry it, and a note is meaningless without the harmony it implies.
All of the many parts of western music serve the harmonic progression. This is because human emotion attaches itself most strongly to harmonic progression, and music is the art of manipulating human emotion through sound.
>A set of great musicians can play a single note for minutes and get it to sound amazing, this has always fascinated me more.
Someone already asked, but give me an example.
>Timbre itself is meaningless without a note to carry it
I suppose that is literally true but I think of timbre (especially after reading Sethares who I mentioned earlier) as telling me about the notes that are brought along for the ride but aren't shown on the sheet music. It's well known that a distorted powerchord introduces a major 3rd (and not the 12TET major third) as well as a phantom or missing bass note and other higher notes which may or may not be perceptible in a given piece. Quite a bit different from what two flutes playing a root and fifth will give you.
Not a one-note solo, but Miles Davis's solo on So What is really minimalistic.
I would actually invert that and say that melody and rhythm are the most fundamental aspects of music. A harmonic progression with no sense of melody or rhythm is quite boring.
Harmony is derived from composing music with multiple melodic parts. This is most obvious with counterpoint, but even pop/rock music can be seen this way. The essence of pop/rock is a melody and bass line as the two primary parts, and the rest of the instrumentation often plays harmonies that imply inner voices.