Traditional jazz bands also preserve the cakewalk music of the 1890's, because it lends itself to the jazz style. Sometimes there is a tenor, baritone, or bass sax added, substituted, or doubled. The best explanation of the differences was given to me in by John Bryce. Thus Louis Armstrong's solos are framed with the pallet of harmonies that are not unlike those of Chopin, Liszt and Tchaikovsky, whereas Parker used the extended harmonies of Ravel, Stravinski and Schoenberg. I find that these later composers are an acquired taste, as is the music of the Bop Era.
Traditional jazz is very much alive, but it is endangered.
In the author's opinion, the music business is based on a triad of broadcast exposure, live performance, and record sales. Broadcast exposure is the key, because it reaches a broad audience and promotes both live performance attendance and record purchases. Because traditional jazz does not get much broadcast exposure, the scope of the market is much smaller. At one time, traditional jazz and swing had the same role in the music business as rock does now. The void was filled by rock, which in its earliest form was an adaptation of boogie- woogie.