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.
Different crowd (fewer suits, less whiskey) but same phenomenon: work deliberately created to be avant garde now repeated as canon.
Before I had status and before I had a pager
You could find the Abstract listenin' to hip-hop
My pops used to say, it reminded him of Bebop
I said, "Well, Daddy, don't you know that things go in cycles?
Way that Bobby Brown is just amping like Michael"
-- Q-Tip, A Tribe Called Quest, Excursions
Of course Jazz greats such as Miles Davis etc would regularly play popular show tunes and use these as foundations for radical reinterpretation (eg. John Coltrane playing "My Favourite Things", Miles Davis playing "If I were a Bell"). If these guys had no qualms doing their own riff on something someone else wrote like "some day my prince will come" I dunno why anyone else should feel they're doing anything wrong doing the same.
Learning songs written by other people is something every musician does. There's nothing wrong with playing covers and being able to play music that's familiar to your audience is essential for many working musicians.
That doesn't mean you have to play old standards when you could riff on newer music, but it also doesn't mean you can't. There's nothing wrong with reviving a tune written a long time ago and putting your own take on it.
Music is not necessarily more enjoyable just because it's brand new. It can be just as interesting if it's new to you, and there's plenty to explore.