When people think "Blues" they immediately think "Blues scale" but if we look at the chords of the blues they tell a very different story.
The chords of the blues progression are all dominant seventh chords, which if we then play the blues scale over the dominant pattern theres a "problem." The scale tones and chord tones clash with one another. For example playing the blues in F, the Ab conflicts with A, the 3rd of the F7 chord, and so forth.
So when we think blues, the question becomes what is the actual parent scale? If we are to stay within the constraints of the chord tones of the dominant pattern?
If we look at chord scale relationships as they are in relation to the basic 1 4 5 blues progression, not to our preconceived notion that blues = blues scale, then the main scale over the blues is actually Mixolydian. As then all chord tones fit squarely within the constructs of the scale. (We dont have to get into other related concepts like the Bebop scales or major blues scale both which highlight the major tonality but with passing tones)
This is relevant because what this means is that the blues scale itself is actually a substitution which creates a certain sound over the blues progression. Tension. Based on the extensions of the chord. An important sound that has a lot of history, and also important pedagogically because if we start a student on black keys the blues scale can be easily accessible with simply black keys with the note A and can lend itself to immediate creation.
Going beyond the blues scale however, to the chord scale relationships of mixolydian, is when we start to get into concepts like: Arpeggiating chord tones, connecting chord tones, bebop enclosure ideas, using scales to create vocabulary, and swapping back and forth between outlining the chords and using scales like the blues scale as vocabulary.
So the blues scale can act as an entry point, but beyond that we can think of the chord tones and scale relationships, in order to go from playing one scale (the blues scale), to playing the changes themselves 😄