There are so many facets to the analogy. One is that much of the great work in both jazz and gca was created long before there were schools dedicated to teaching those arts. In New Orleans in the early 1900s, there was not much love between black musicians and Creole musicians; the latter tended to be schooled musicians, often classically trained, and they tended to look down their noses at blacks like Louis Armstrong, who learned and played basically by ear, and who took whatever their predecessors could teach them and moved on -- or not -- from there. And even after Louis made the revolutionary Hot Five and Hot Seven recordings in the mid-to-late 1920s, the attitude persisted. While his new found acclaim got him passage from Chicago to New York and a seat in Fletcher Henderson's then-famous big band (an all black band playing to New York's white society set), there are many stories of the Henderson band-members making fun of the 'country bumpkin'. (There is an oft-told story about Louis trying to read one of Henderson's scores, sight-reading the music for the first time: when he and the band got to a section marked pp for pianissimo, Louis started playing as loud as he could, and when Fletcher stopped them and asked why Louis was playing the pianissimo so loudly, Louis replied "I thought pp stood for pound it plenty".) The mocking stopped after a short while, when the band realized Louis' genius and inventiveness as a soloist and improviser, but my point is that Louis Armstrong wasn't consciously thinking about "creating the language pf jazz" (as he is often credited, probably rightly, with doing) -- he was playing what he'd heard on the streets and in the nightclubs and then transmuted through his own personal talent and taste. It took teachers and critics of a later generation to write down and explain and codify what he'd been doing for so long. I think this partly explains why many of Armstrong's best solos sound as fresh and appealing today -- even after 90 years -- as they must have back then, while so many of those well trained and well intentioned musicians who try to pay tribute to his music sound so forced and even corny.
Peter
PS - I remember reading about a study that a couple of jazz egg-heads did in the early 1950s. They studied a hundred of the best jazz solos up to that point, and came to the conclusion that a great solo tended to have musical choices (note and rhythmic selections) that were 50% expected and 50% surprising. Now imagine a nerd like me taking that information and trying to play a solo while all the time thinking "I must make a surprising choice here, followed by a conventional one...no, wait - two suprising choices and then two conventional ones....". What a recipe -- or, in gca terms, rule -- for disaster, eh?