But practically and musically, it was used for the sixth chord and dominant 13th and 9th chords it gives.
So practically and musically, it is obviously an E tuning. Do people play Amin7th pedal steel, or C6th?
It was called C#min because that was the most obvious name in the early 30s when the sixth chord wasn't really a recognized thing not because it was mostly used for minor chords.
(see how Alkire calls them "major added 6th" above. I doubt many would call them that today).
The minor triad is a big deal because the inversions of E C# G# E also spell great straight bar and slanted major and dominant chords.
Compare that to a tuning that is actually minor like hi-to-low E C A E C A (A high bass with the C#s lowered) and the usability in comparison plummets.
You don't need straight bar minor chords to play good minor music : https://www.youtube.com/watch?v=okT4JP3Vjx0 (Jim and Bob - St Louis Blues)
The chords that the C#min tuning gave happened to fit in with general trends in music in general at the time, when 9ths and 13ths sounded modern.
When replacing all your major chords with sixth chords sounded hip, just as it would be with major 7th chords a decade or so later.
I have the book in the OP pic "Mills Radio Favorites for Guitar Volume 2" (also vol. 1) and most of Sol Hoopii's C#m arrangements published by Roland Ball and 80%+ of the time chords on the top 4 strings are dominant and major chords, for example.
It is a happy accident that the A pedal gives a C#m. It came from splitting the Bud Isaacs pedal which rose G# to A and B to C# at the same time on an E9th tuning:Aaron Brownwood wrote:Correct me if wrong. But I like to play C#m and E7 just by changing the C# down to B. This is where the A pedal on PSG comes from essentially. Retuning E7 to C#m.
E
B -> C#
G# -> A
F#
D
B
G#
E
Curly Chalker on his Fender 1000 at the time instead had the Isaacs pedal on Leon E13th (but tuned up to F) so he could still have the 13th open:
E
C#
B ->C#
G# ->A
F#
D
G#
E