I don't think you're being fair to saxophonists. Compare them to the pianist, bassist and drummer who get to play for the entire piece! The saxophonist patiently waits to solo, with nothing to do but ...
Clarinet and trumpet were king in early jazz backed by big piano, trombone and rhythm. Saxophone was a buzz in, out and at times sounded like a zombie lurking in a boiler room or a troll trapped in ...