Riemannian functional harmony is derived from heptatonic model of music, tuned to meantone (while heptatonic 5-limit music can be tuned to other temperaments where other chord progressions, not possible in meantone without enharmonics, can be realized). And it's not even capable of explaining like 1/5 of the progressions in romantic and modern period (which on top of that require enharmonic modulations in meantone (that's one of the main motivations of Neo-riemannian theory - to explain chromatic harmony in 12 equal.))
Imo, figured bass as an idea is more useful model for pure intonation music - over a bass note you can build a major or minor chord, or any of its inversions, and harmonize to your musical taste.
I doubt Bach was understanding his music in "functional sense" - this makes no sense, considering when this theory was invented and popularized, but certainly there are chromatic passages where he was using his "well-temperament tuning" in chromatic (12-tone fashion), not heptatonically.
Even, if this is slightly off-topic, since Million likes scale models, let's do one -
Regardless of tuning, here is quantization of some of the most useful for harmony and melody 5-limit limit ratios, reduced to heptatonic model:
I. 1/1 -unison, 25/24 - chromatic semitone (this means that this semitone is tempered in 7 equal and, in accurate systems, you use it for modulation to other keys; obviously, diatonic and chromatic semitones are equated in 12 equal, potentially giving us the option to play confusing for the listeners tonicizations, not knowing, if you modulated or not)
II 16/15 - diatonic semitone (inverse of 15th octave reduced harmonic), 10/9 - minor whole tone, 9/8 - major whole tone (octave reduced 9th harmonic)
III 6/5 - minor third, 5/4 - major third (octave reduced 5th harmonic)
IV 32/25 - diminished fourth (inverse of 25th harmonic), 4/3 (inverse 3rd harmonic, reduced to octave), 25/18 (augmented fourth).
And that's it - you can get fifth, sixth and seventh degrees by inverting these modulo octave.
So, we get a heptatonic scale with variable scale degrees that can be useful for creation of most ethnic and non-ethnic modes in 12 equal (useful technique is using these as melodic tetrachordal blocks, giving us Arabic/Hindu/Greek take on scale construction, obviously playing alterations of the same scale degrees can sound potentially bad ).
Tempering 81/80 gives us a regular temperament and the ability to play meantone progressions (like the infamous in jazz 2-5-1 chains)...
Here is the interesting part - we can quantize pure ratios to different (and they are not unique and there may be several such options for creation of abstract temperaments - check 17 equal for example, 17 tone scale can be mapped in several ways to 5-limit) pentatonic, hexatonic, octatonic, nonatonic etc hierarchies (think of black keys pentatonic, found in Eastern and African music; or some of the synthetic scales, used by Scriabin, Liszt, Stravinsky etc), giving us different perspectives on the usage of abstract temperaments/scales. For example here is a pentatonic one -
I 1/1, 16/15 (diatonic semitone is a chroma!)
II 25/24, 10/9, 9/8, 6/5, 32/25 (!!!)
III 5/4, 4/3, 36/25 (!!!)
It doesn't look as pretty, giving options for improper and monotonically not ascending scales, but let's for examples check the intervals in the black keys pentatonic.
II 3 x 200.00000 cents
II 2 x 300.00000 cents
III 1 x 400.00000 cents
III 4 x 500.00000 cents
IV 4 x 700.00000 cents
IV 1 x 800.00000 cents
V 2 900.00000 cents
V 3 1000.00000 cents
Number of different intervals: 8 = 2.00000 / class
All this theory is backed by serious math (mainly linear and exterior algebra). (And can be useful for composing music/translating existing in/between different temperaments + just intonation)