Thing about the sax is that it weds itself to two ethnographic classes: it is a brass instrument with a woodwind principle. What better way was there for Avant Gard practitioners of soul, jazz, and blues to find a voice not limited by woodwind or confined to brass!
Yes! What HF said, but I will add I lived in Deep South Mississippi in the early 60's, which is considered the birthplace of the Blues! I remember the Miles Davis band and those now-legendary musicians in the prime of their careers: tenor saxophonist John Coltrane, alto saxophonist Julian "Cannonball" Adderley, pianists Bill Evans and Wynton Kelly, bassist Paul Chambers, drummer Jimmy Cobb and, of course, trumpeter Miles Davis!
May I say, you seem quite comfortable in any idiom -- whether spiritual, world-wisdom wise, or idiomatically musical. You've spelt out the names of many legends, among whom I regard Coltrane and Davis to top the list.
The saxophone has always been dear to my heart. You may see what I've said to HF on the subject of classification.