I recall most of those big bands as they were current events for me. I would expect they were all connected to their own history better than most and, able to make use of old learning. I saw the movie about Mozarts life and wondered how many details there were to coordinate where you have a large number of instruments playing how many different notes at what intervals--the number of combinations is hard to imagine but he was able to write it all down and have it come out right without editing which would seem
impossible. I tend to favor the idea that there are no prodigies --they worked on these talents long before current times. While not many are in such a class as Mozart, they are to some degree similar.