stuartk, I don't think their art/music has to do with their personalities. I could use actors as a comparison. Personally, some actors are quite modest while others like to fill a room full of people at a party. On stage, they all must "swagger," whether that means playing a timid part or large part.
You think about a musician improvising, they have to bring out their inner musical "swagger." (Perhaps a bad word.) In the documentary on jazz, Wynton Marsalis said that jazz was about the musician showing their "personality." And perhaps that is a better word than swagger. He used a very interesting metaphor of a writer and a pencil. The pencil doesn't write the story, the writer does. He was talking about Buddy Bolden who is considered the first jazz musician. Marsalis said that Bolden's coronet did not play the music, Bodlen did. And apparently he had plenty of swagger.
One other thing about the first episode of the documentary "Jazz" that really struck me was that for about four decades jazz was the most popular music in the country. That's when people could dance to jazz. I think somewhere in the fifties (after Parker?), it became more cerebral and the mass audience went elsewhere, to rock n' roll, I would guess. Although some jazz players, most of whom I think would be eschewed in this thread, like Diana Krall and Herbie Hancock (he played the tribute to Joni Mitchell in the Hollywood Bowl), most jazz players play in small clubs to a selective, more "cerebral" audience who aren't dancing.
Although I like straight-up jazz (I was playing an album of Tina Brooks yesterday), i love jazz that has a dance beat and makes me want to get up off my chair. Lizz Wright has that quality. Here is an excerpt from a review about her in Downbeat:
"Lizz Wright comes to her music with equal parts gospel, jazz, r&b and blues. The alto vibrations of her dark-toned, rich voice would sound at home in any church, jazz club, theater or even arena. She’s just that versatile as an artist."