When you try to make theoretic sense of a Blues it doesn't usually work out to well. If you had a time machine and went back to Bach's time and explained (in German) in pure theoretical terms about this style called the Blues, he would probably think you a nut case. Of course we know from playing it and listening to it, it works out pretty well though, at least to our modern ears.
It is sort of diatonic and I say that because it is based on the I, IV and V chords of one key. The "sort of" is because we change the I and IV chords to dominant chords. If St. Peter wouldn't let me through the pearly gates unless I could explain why the I chord is dominant in the Blues, I suppose I could tell him that it sort of functions as a V/IV chord. Right? a C7 in the key of C is the V chord of the IV chord. C7 goes nicely to F, a secondary dominant chord.
The dominant IV chord can't really be explained but if I had to come up with some sort of explanation at gunpoint, and I'm not really sure this is right, but I would say that as we like to play a minor pentatonic scale over the progression, the minor 3rd in the scale, is the b7 in the dominant IV chord. Right? the Eb note in the C minor pentatonic scale is the b7th of an F7 chord. Maybe that has something to do with it, but I'm not sure. The dominant V chord doesn't need much explaining.
All in all, the truth is that slaves liked the way that the minor pentatonic scale sounded of the white man's I-IV-V progression. And the major triads eventually turned into dominant chords. Maybe because of the b3rd in the scale but that is just a guess on my part.