Classical training is a different story. Musical theory is endlessly useful to know. But jazz has been stuck in a certain kind of sound for the last 40 years since those people who actually made it gave way to those who simply play it. And now there's just this idea of what jazz is and ought to be, rather than treating it as what is was originally; a complete break from the roots of the western classical tradition into a wholly new art form informed by the limitations of what they were leaving behind.
It's sort of a cargo cult situation, really. You have these incredible artifacts left behind that came about as a result of complex processes of intense effort and struggle, yet those who inherited them act as if by imitating the same thing, they will get the same results. It's completely missing the point.
Wait, what? A whole lot of the western harmonic tradition went right into jazz. The "standards" are Tin Pan Alley songs from the first half of the 20th century. A lot of the bebop harmony came straight out of Debussy and Ravel. Third Stream music was an explicit synthesis of classical music and jazz. Some of Coltrane's innovations came out of Nicolas Slonimsky's Thesaurus of Scales and Musical Patterns. The walking bass was in Baroque music (Bach). While you cannot neglect the African side of it (rhythm, the blues, improvisation) nor neglect that it was Black people who put together the pieces and created the music, saying that it was a "complete break from the roots of the western classical tradition" is farcical.
And it's a tradition, not a cargo cult. There are still people alive today who played with Miles Davis, Charlie Parker, and so forth. I have played with some of them. They tell stories, give advice, and pass on things that you might not get otherwise. Before the advent of jazz programs in colleges, the music was passed on via an apprenticeship system, which is diminished but still extant.
Today, people approach jazz for different reasons, and of course at different levels of proficiency. Jazz is old enough to have a history and a canon, and the enjoyment of exploring and preserving that history is a good reason for some bands (hopefully not all of them) to exist. Given my stature in the local music scene (not a first-call player), a lot of my work is of that ilk. I approach it respectfully but not with utter obedience. As a bassist, the instrument that I play has undergone steady evolution, even post jazz era, so that what I play on a "traditional" gig is informed by the present as well as the past.