this is fascinating.
fwiw, I do improv comedy in Chicago (team at iO, indie trio and team at CIC). it's really interesting to read how others interpret that work from other improvised disciplines. particularly striking about the back and forth above is the focus on narrative and that improv comedy has something to teach about it.
there's actually been a huge shift in improvised comedy away from improv serving ANY sort of narrative. the best shows I've seen have teetered on the brink of absolute nonsense -- the joy of being audience to these pieces is watching human beings listen and react honestly to each other as human beings. specificity and detail help the improviser to clear up ambiguity and PLAY, but any explicit focus on or leveraging of external factors or events or "inventions" that are intended to provide narrative structure to help make sense of what's going on will 9 times out of 10 tank the scene. in that world, an audience isn't interested in being able to walk out of a show and say "oh, that made sense. I understood what was going on." as soon as a show tips that direction, you're just watching performers fumble through already known plots and situations instead of human beings. and you could watch the former on TV, so coming out to see it live is a waste of time.
to that end, the best and most worthwhile shows are usually the ones that an audience member could NEVER explain to their friends. "this one guy just yelled 'oh god, oh boy' for two minutes over two other people who were dead" doesn't capture the absolutely blinding brilliance of watching an improviser MAKE THE DECISION to react to the deaths of his friends in this way. it is the decision, to watch a human being arrive at a pure impulse and follow through on it, that is so much fun.
Herbert Brun wrote about jazz pretty severely because when he watched the performers, he could see and hear that they would eventually just cycle through aural touchstones -- this lick, that motif -- rather than allow themselves to be human beings (with instruments) listening and reacting to other human beings (with instruments).
tldr; the liminal quality of improv comedy (and its ability to support narrative if necessary) is not so much a hallmark of its current strengths. in fact, it's become increasingly post-form, hinging on behavior making a show great rather than its concrete understandability. improvised music, which has less liminal tools in its corner, might be less able to break
form and still be appreciated by its audience (who is maybe still trained to 'understand' music). so maybe music improvisers need to push themselves to (as identified in the original piece) listen more purely, react more honestly. then, the self-supplied pressures of form and tradition become less validating -- as the ego removes itself from the process.