The primary face of Jazz stayed black for one reason and one reason only: Miles Davis, but even then the genre had become watered down in the 70's when the fusion style of jazz came in, and that was basically white guitarists wanting Jazz credibility without applying themselves as creatively as the purer jazz musicians
But the thing about Jazz that's different from any other genre, it's forerunners always gave credit where credit was do, whether black or white. Nobody ever hid behind a fanbase or took credit for anybody else's work....but a lot of that had to do with those old timers being willing to throw down during that era over that type of stuff
But you can't look at what happened to Jazz the same way as what happened to Rock N Roll. Jazz became an international force and had a level of comraderie and unity that no other genre was able to achieve. Besides, the best bass guitarist of all time was a white man (Jaco Pastorius)