It's because symmetrical scales are parental forms. They have properties that non-symmetrical scales don't have .
For instance, if we look at the whole-tone scale, we can split the chromatic scale into 2 different 6 note whole-tone scales:
G A B C# D# F
C D E F# G # A#
The whole-tone scale is connected to the dominant function.
Consider: G 7 from key of C major:
G is root
A is 9th
B is 3rd
C# is #11th
D# is b13th
F is 7th
But look:
GBD#FAC# = G9#5#11
But because the whole-tone scale is symmetrical, we have connection to
6 major keys (i.e. to the dominant function of 6 different keys)
G9#5#11
A9#5#11
B9#5#11
C#9#5#11
D#9#5#11
F9#5#11
This means that now we have a parental form with G wholetone ( 6 sep dominant functions from 6 keys).
But it does not end here.
Consider the other whole-tone scale we didn't use:
C whole-tone
C D E F# G# A#
Any of the dominant chords from the first whole-tone scale can resolve to any major or minor chord built from the tones in the second whole-tone scale. That is, these chords:
G9#5#11
A9#5#11
B9#5#11
Db9#5#11
Eb9#5#11
F9#5#11
can resolve to any of these chords:
C major or C min
D major or D min
E major or E min
F# major or F# minor
G# major or G# minor
A# major or A# minor
Each symmetrical scale as a parental form, in its own unique way is a larger structure then a key.
If we look at the diminished scale, say:
G HW diminished or GG# A#B C#D EF G
It contains the chords:
G7 GBDF
Bb7 Bb DFG#
Db7 DbFG#B
E7 EG#BD
These dominants are related.
G7 is the V7 of Cmajor ( G7 to Cmajor)
Db7 is tritone of G7 ( Bb7 to Cmajor)
E7 is V7 of Aminor ( rel minor ) ( E7 to Aminor)
Bb7 is tritone of E7 ( Bb7 to Aminor7)
This is how all 4 dominant work in C major however this works same exact way for
Key Cmajor, Key of Ebmajor, key of Gbmaj7,key of Amajor
So this symmetrical scale is parental form that connects a relationship of dominant function between these 4 keys .
All symmetrical forms have their own unique relationship.
Non symmetrical scales do not have nearly as much interesting about them .
Lastly, no matter what key your are working in (in a specific context), for example C major, you have strong beats and weak beats of the bar .
Strong beats are always chord tones and weak beats are embellishments, so all 12 notes are there to be used. That is how the chromatic scale directly connects to any situation.