I clearly know nothing about music, but why does it even have to be called 'Jazz'? Given those market numbers cited, it seems like it would be a very bad brand to be associated with your music. Having a son who's 12, and having recently had a bunch of pre-teens running around my house all going through the timeless ritual of identity crafting, I have gotten to listen to their music, watch their media, and hear their…
This isn't new. There's the oft-maligned Latin Jazz---one reason a lot of synthetic music that happened in Cuba, Brazil, and other such plays was more similar inputs---similar outputs development in parallel. Once you get recorded music + radio, and tourism in Cuba, there's more actual cross-pollination, but there's plenty of stuff before that.
As far as the method goes, obviously improvisation is a big part, but the big picture is Jazz is a social and live music. If Classical is a play, Jazz is a conversation at a Cafe. Sure people listen to recordings, but also classic trane records and others are a lot more sliced and diced than one might think. There's big band too, but what goes on at most schools is a bit suspect without the collectively authored head arrangements. Musically, we have the tradition of a preset harmony and, to a lesser extent form, is the "seed" for everything else, African rhythm, European harmony, and a bunch of unconscious idioms that would be hard to right down without lots of luck and pondering. [There's my cop-out. :)]
As a younger student, I and many others gravitated towards funk, because it's clear (though nobody said so explicitly) that that is the foundation for everything that's popular today (more than rock I'll jeer now that top 40 ate everything :P). The narrative of funk, if you will, is soul musicians' session players striking out of do their own more instrumental/dance focused thing. And those session musicians all had jazz backgrounds. So there's the historical connection, and musically it's largely a similar method, though more emphasis on premeditated groove and rhythm section in general.