My first impression on seeing Whiplash was that either Chazelle doesn't understand jazz, or he's painting a devastating portrait of a Hitlerian father figure who triumphs in the end by making his surrogate son as much of a fascist as he is.
I wasn't sure at the time which direction Chazelle was pursuing, but after seeing La La Land, I decided he simply doesn't understand jazz, just as he doesn't understand Hollywood musicals (or the importance of thematic development and character arcs for telling a good story).
Jazz and blues are probably the genres most inimical to rigid formalization. They constantly exploit the conflict between structure and free play. The music played by the ensemble in Whiplash is incredibly precise, but it has no air, no grace. It's not a White jazz vs. Black jazz problem. Sure, John Coltrane, Charlie Parker, Thelonious Monk etc. play with a swing that's missing from the Whiplash approach. But there are just as many White jazz musicians (Conte Candoli, Billy Butterfield, Stan Kenton...) who avoid the lockstep timing of the ensemble in this film. Even Henry Mancini is cooler than J. K. Simmons' character.
If I'm wrong, and the theme of Whiplash is about how a domineering authoritarian can stunt the growth of a young acolyte by infecting the student with his soulless rigidity, then the movie is just too dark for my taste.