A first question which comes from here:
Yes, the Roman Numeral, 'vertical is all' system derives from Rameau, or at least the interpretation of his treatise by Marpurg, though I don't think numerals were used until later.
Sorting this out: Are the things you are objecting to or have collided with - are these Rameau himself, or
what has been done with Rameau? This is an actual question, not rhetorical, since I'm just getting into this world. Does anyone (did anyone) ever "teach Rameau", or were there teaching systems that were devised from Rameau's thoughts. This is probably important.
My own journey: I dealt with music for 40 years via the "movable do solfege" that I had gotten one year as a child in primary school; it was that, and what I had sensed in music from playing and listening using it - mostly nameless and instinctive. When I finally took formal lessons (violin) I ran into things. It started when I checked my singing against the piano and my "Ti" was "too high" and my "Mi Fa" were different. Of course there is a reason for that. My sense of how music works had been strongly formed by all the Clementi I'd played when young (i.e. what I had at hand in passed on music). The sung "Ti Fa" had fused with the V7 chord (which I didn't know about) making me hug those two notes closer than a semitone to "Do" and "Mi" respectively and I was sensing the cadence. I was told that in the melodic note names I was hearing the harmonic progression. You may be able to make sense of this. I can.
The "simpler" music we encounter - unless it's pop - goes along these same constructs, and the music for teaching an instrument generally does too. So we're in that box where everything fits together. I didn't really know notes - My reading was part anticipation of "where the music should go", part seeing broad patterns like a straight line of notes is a scale. To the point that I didn't know I was not really reading music. That was discovered by chance in a lesson.
I studied theory rudiments starting with note names; 2 months later I aced the 2nd level exam with a grade of 100% and passed the advanced level 3 months later with a high grade. Everything in RCM rudiments fits hand in glove with my old solfege and Clementi world, plus I was actually hearing it from sight singing for decades. When first learning a construct of scales, you religiously mark in all the Tonic and Dominant chords. (My So Do). I had the advantage that I also thought melodically. (The thing you see as missing).
Next I went on to harmony theory proper, but asked in the store for a book that was "not written for passing exams, and had depth". I was handed a 1947 Horwood, where you see the figured bass that was absent in the standard books (the revised version now includes it). Again it fit hand-in-glove with my m.d. Solfege /Clementi world. At some point elements were missing and I bought two more books - Sarnecki, and another that had many examples from actual music and insisted that students play and listen as well.
As I was doing this first harmony theory (no longer taking lessons), I met my present piano / music teacher. I wasn't studying with him yet. He warned that these systems could put me into a box. We worked on much of this together, also looking what was in there. The exercises often would not allow you to make decent music because they were poorly written, and you were straightjacketed by using only what they presented. And then, for the "examples taken out of music" (20 - 30 per chapter), if you knew the music from which the examples were taken (as he did), often a small segment was taken out of context and twisted to fit the theory. It WAS good to see the general principles and this HAS helped me. But with the precaution that "this is part of the picture, much (some) of the time."
We broke off and looked at Chopin, first off, and used letter name chords where "it is what it is" without category. We went at what was actually heard and going on in the notes. It was largely unstructured - things pointed out as they were encountered. An experiment with no rigid system. You do notice raw patterns: music does contain cadences, and where a pattern repeats itself in another key and varies, these patterns are good to know about and use.
I'll note that this was still largely via chords, but it was also via horizontal movement; again on the surface via the movement of the chords. But you're also looking at other things: what is happening with the bass line - is it going chromatically, leaping in 4ths and 5ths; is the main melody line slithering in semitones - how are the middle notes sliding or jumping or colliding?
In regards to Roman Numerals: There are places, as in a rough outline, where you have your Tonic and Dominant, and your "chord notes". It is handy to see the I's and V's where they occur, and to see new V7-I's where it modulates in true modulation or a temporary tonality. But trying to squeeze every single beat into a Roman Numeral puts you in a box and keeps you from what is there in the music. It becomes hugely complex.
Other things in music - you see them happening, you understand them - don't fit with chords for understanding them.
From this side of it, my overall thought is that music has numerous angles, and no one system should be used uniquely to try to understand what is going on. That is as far as I got.