The same why that Rock did, or Ragtime, or impressionist art, or anything else. Eventually it's accepted and then appropriated by the mainstream establishment. At which time it's typically sanitized and made more appropriate for the masses (where it, arguably, loses its connection to its original intent and meaning), and gains mainstream acceptance.

Jazz was known as being very experimental, with everyone adding their own flair to it. It evolved from a very simple blues core into some really crazy, blisteringly fast, fusion jazz in less than 100 years. In that time, it also split off into a TON of sub-genres.

A lot of the jazz we hear comes from a style called Bebop. Your Charlie Parker, Dizzy Gillespie, Charles Mingus. It's improvisational, fast, and many people consider this style, very popular in the 1940s to be the peak of Jazz.

During that time, you saw Big Band music, which was jazz as well, but moving away from the "hot jazz" tradition to what is called "sweet jazz". Sweet jazz would have a much lighter sound, slower tempos, suitable for slower dancing, softer instrumentation, and was essentially whitewashed jazz for the masses. And sweet jazz was more frequently performed by white musicians, and for white audiences. Prior to the 1930s, jazz was very much considered a black person's music.

This is when you see the Tommy Dorsey, Benny Goodman and Artie Shaw types come around. All playing super light, slower, jazz for white people. This type of jazz, because it hit not only the dance halls, but the radio waves took off, and you saw decades of this kind of slow, sweet, dance hall type jazz playing everywhere, even into Frank Sinatra, Lawrence Welk and others. It was inoffensive, light, easy listening, and so became popular.

Jazz itself continued to evolve into Post Bop, Free Jazz, Fusion Jazz, and so on, with Miles Davies and John Coltrane and the like, but it's a different branch of the jazz world. It's still around, and people are still playing it, and it's definitely not mainstream or accepted.