The radicalisation of the picture plane from a three dimensional to two dimensional 'surface', should not be equated with a move from 'harmony' to free. The difference between Coubet and Pollock is far greater than the distance between Parker and Coleman.
'Art' has always been the domain of the rich and powerful be it practitioners or academics. Jazz developed in far different circumstances.
The history of Art avant-garde negations has and did serve different purposes to those eminating from a specific Black cultural expression in the more compacted social and formal history of Jazz.. Just look at the exclusion and distance Black people have had in 'The Visual Art Story'. Because of social segregation and poverty just to begin with.
So called traditional Jazz improvisation and harmony has far greater relevance to the forms and considerations of 'pre-Modern Art' if only in terms of it's huge depth of skill and muscle memory construction - than it does with the Formal 'dumping' of 'Abstract Expressionist' painting, where visual integrity is achieved more through stealth than through preconcieved rules and knowledge.
One interesting comparison however might be in the cut between the History of Visual Culture to be adressing 'Nature' and the Modernist turn to be addressing 'Culture'.
ie. the 'fully played out and explored' domain of Harmony via Bop and Modal as 'Nature' as opposed to a Free Jazz expression as a 'Representation', where Culture has primacy over Form. As in the perjorative arguments the anti-Shorter guy was making. Whereby he was saying Shorter was merely 'representing something - "Culture' - rather than actually playing something real, ie 'Nature'.
Then we have 'two' kinds of representation of 'Culture'. In the differing ways an Evans might be representing 'Culture' - as opposed to the way David Murray might be representing Culture.