Charles Mingus might be the ultimate example of someone who's "jazz famous." Within jazz circles, he's revered, but he should be as well-known as Miles Davis, Duke Ellington, or John Coltrane. His name should be as familiar as theirs to people who know almost nothing about jazz, but it's not, for a variety of reasons. He had a volcanic temper that was at one time or another turned on almost everyone in his personal and professional life — bandmates, record labels, managers, wives (he had four), even audiences. He famously destroyed a bass onstage at the Five Spot in response to heckling from the crowd, and punched trombonist Jimmy Knepper in the mouth during a rehearsal, knocking out one of his teeth and ruining his embouchure.
