Why have so few rock groups been racially integrated?

Why have so few rock groups been racially integrated compared to jazz bands? After all, Benny Goodman featured an integrated orchestra in the Thirties. Before the civil rights revolution, black and white jazz musicians put up with all sorts of nonsense in order to play together. When Charlie Parker's band toured the segregated South in the Forties, they told local sheriffs that their white trumpeter Red Rodney was actually a black man named "Albino Red."