Since I'm in basic agreement with the rest of your post, let me comment on just this one question.
TN note naming, so far as I understand it, it based on the spiral of 2:3 ratios, and the seven-letter note naming scheme. So after cycling from F C G D A E B you encounter a note between the F and G (an octave or two higher). What to call it?
it you are going "up" you call it F-sharp. Then next time around, the note between F-sharp and G-sharp, we call F-double-sharp. [Why not G, you may ask? Because it needs an "F" letter name to preserve the 7-letter sequence.]
Going the other way, "down", after B E A D G C F we encounter a note between B and A. So we call it B-flat;
next time around, we encounter the note between B-flat and A-flat, so we call it B-double-flat. Etc.
Ok, so this whole scheme is based on 2:3 ratios and 7 letter names. Counting the 2:3 interval on the diatonic scale spans 5 notes, so the interval is called a "fifth", which makes "perfect" sense in diatonic reckoning. In ET, this ratio is approximately 7 half-steps. It is possible to build a scale from five consecutive pitches in 2:3 ratio, with their octaves.
We call this the pentatonic scale. But the scales built on G# and Ab are not the same frequencies, if you "do the math".
Now lets proceed to classical harmony. I've heard it arose in England. They discovered the intervals of 4:5:6,
the major triad. By reversing the intervals (5:6, 4:5) we get 10:12:15, or the minor triad.
On the diatonic scale, these intervals are 3 (diatonic) notes apart. But 4:5 and 5:6 are not the same sound. (On a piano,
they are either 3 or 4 ET notes apart.) So we have "major" and "minor" thirds.
What's more, you cannot get "thirds" or 4:5:6 from the pentatonic scale, because 5 is relatively prime to 4 and 6, i.e. to 2 and 3). No multiples of 2's and 3's will ever give a multiple of 5, and vice versa.
So consider the Tonic triad on C. The unison and fifth are the C and G of the pentatonic scale.
But what about the middle note? It is "close" to the pentatonic "E", but not exactly. For the minor triad, same story for the "C" in A C E. So what should we call this note? For now, let's just call it Note-prime.
Now we can form a major scale from three major triads (and their 1:2 "octaves"): F A' C E' G B' D
(which is traditionally written starting on C.) Or, we could use minor triads: D' F A' C E' G B' and get a minor scale.
And let's try the dominant of C: C E' G B' D F#' A
So put it all together: D' F A' C E' G B' D F#' we end up with notes from two different interlaces spirals of fifths, with two flavors of "D" (re) [Sometimes you will see a circle-of-fifths written with major chords on the outside and minor chords on the inside, which is an accurate picture as far as it goes, if you recognize the F# is not Gb but two distinct ends of a spiral that wind around forever in both directions. (There are many examples on the internet of the "spiral" of fifths, but a quick search didn't turn up any examples of two interlaced (major and minor) spirals. Guess I'll have to create my own.)
Now, if we include the tritone in the dominant 7th chords for G in the major, D in the dominant, and E in the minor,
we get some extra notes F" C#" G#" from different spirals, depending on how you define the tritone. (Some define it as a minor third 5:6 from the fifth--which can be read from an extended Tonnetz; some as 4:5:6:7, etc.)
Now notice that, except for the pitches D and F", all the scale notes are distinct, so we can tune an instrument to play songs in just triadic harmony as long as we stick to a single diatonic key. But if we want to combine say a D-minor and G7 chord in the same piece, we have a problem. (Notice that the first prelude in Bach's Well-Tempered Clavichord begins with a Dm7-G7 progression.) Today, of course, in ET, the ii7-V7 progression is pervasive.
But even more seriously, TN naming does not really distinguish between minor and major thirds.
It's true that minor and major chords have different note names: C E G is major and C Eb G is minor--
but what about C# E G or C E G# or C E# G etc. What about D F A vs E G B vs F A C ?
The problem is the A B C D E F G sequence "reads" like equally spaced intervals, but it's not.
We know that there is no note between EF or BC. There is indeed an E# and an Fb, a B# and a Cb, but they are not "between" but "on" the neighboring note.
Just looking at the letters of a given chord, you can't readily tell which intervals are major and which are minor.
The spacing of letters may be the same but the intervals are different; the number of accidentals is not a reliable clue. You just have to know where the "half-steps" occur in the letter sequence, and do a calculation.
It just amuses me when people get so indignant that ET notation obscures the distinction between G# and Ab
(which seldom occur in the same piece, although they theoretically could) but are unconcerned that TN obscures the distinction between major and minor thirds. Furthermore, if "just intonation" is their concern, why no concern about the difference between what I've called D and D' or F and F", which occur routinely--though perhaps not in music written with just intonation in mind.
It's like debating the virtues of butter vs margarine for your toast while ignoring the difference between wheat and rye,
or bagels vs muffins.
So i'll let you answer your own question. In that TN note-naming obscures "thirds" harmony--
"equalizes" the difference between major and minor thirds, and does not distinguish the "major" and "minor" spirals--
and given that "stacked thirds" is the basis of classical harmony, does TN naming do a good job?
The distinction between major and minor thirds provided by ET (12-step) notations, in my humble opinion,
is vastly more useful, in terms of harmony, than the distinction between G# and Ab. The only thing we would lose my moving to a 12-name or "dozenal" naming scheme and staff from traditional is familiarity. And, with use, the twelve-step scheme would become familiar quite quickly.
Joe Austin