Does this Bach Cadence have a name?

Does this Bach cadence have a name? It is from J.S. Bach, the 3rd violin partita, BWV 1006, measures 25-27 (you can download the complete score on IMSLP):

It appears to consist of an arpeggiated seventh chord built on each scale degree of E major in the circle of fifths, starting on the seventh degree:

• vii^ø Locrian [D#halfdim7]: D#-F#-A-C#
• iii Phrygian [Bmin7]: G#-B-D#-F#
• vi Aeolian [C#min7] C#-E-G#-B
  
• ii Dorian [F#min7] F#-A-C#-B
  
• V Myxolydian [B7] B-D#-F#-A

The full piece (Gigue) is here:

 

I've been fascinated by this progression for some time. It seems to be a very simple progression based on the modes from dark to light. I've only ever seen modes discussed in terms of "bright to dark"; for some reason, various music educators recommend practicing the modes in that order. But light to dark is retrograde to how Bach uses them here; since ii-V-I is contained in the progression, it seems dark to bright should be the prevailing order. In any case, nobody seems to offer any practical use for this progression.

In the key of C, the diatonic progression in full would be as follows:

• vii^ø Locrian [Bhalfdim7]: B-D-F-A
• iii Phrygian [Emin7]: E-G-B-D
• vi Aeolian [Amin7]: A-C-E-G
  
• ii Dorian [Dmin7]: D-F-A-C
  
• V Myxolydian [G7]: G-B-D-F
• I Ionian [CMaj7]: C-E-G-B
• VI Lyidan [F7]: F-A-C-E

The complete cadence follows a very simple schema of seventh chords build on the diatonic circle of fifths, from "darkest" to "lightest" modes:

B-E-A-D-G-C-F

To repeat, the ii-V-I progression is a fragment of this longer progression; it must be a very ancient or mathematically primal progression. But what are its practical uses? Who has employed it besides Bach?

A related question I have often wondered, that I have never seen addressed in music theory or by music educators, is why A-B-C-D-E-F-G was not used to designate a major scale if major (Ionian) is the default scale?

If tones are to be named after the first seven letters of the alphabet, it stands to reason the A Aeolian (A minor - A-B-C-D-E-F-G) is the default mode of Western music (not C Major). Why else would you use the alphabet in such a way? It makes no sense if a major scale is the default mode to deploy the alphabet so that scale reads from C to C.

Presumably, this anomaly marks a shift in Western music as the default mode in ecclesiastical music (Aeolian or natural minor) shifted to military music (Ionian or major), and the emphasis on church shifted to state. But no one addresses this curious musical question that I'm aware.

(I have read some remarks that low A was the bottom of the range of some singers' voices, and that this lead to arbitrarily deploying the alphabet in that manner. But this is a stupid, unconvincing, and wholly insufficient explanation.)

Note: Don Simpson has a PhD in art and architectural history and is a lifelong student of music. He plays clarinet, tenor saxophone, and guitar. Some musical terminology may be inaccurate or nonstandard since he's also a dumb comic book artist.