"Not just technical facility but also the brain connection with the arm muscles so to speak, developing that facility to the point where the subconscious mind can take over the basic mechanical task of playing, thus freeing the conscious mind to concentrate on the spontaneous development that distinguishes the best jazz..."
Arguably, this is a prerequisite for performing ANY style of improvised music well.
It’s pretty hard to stay "in the zone" while switching back and forth between right and left brains.
Your topic brought the following to mind:
"Just a little more and this instrument is gonna be so connected with my brain that my fingers aren’t gonna have to play it"
-- Duane Allman