Jazz metal is an oxymoron
Pretty much.
I'm a much more experimental jazz type guy--no I-II-v, no standards, etc. and pretty much start my jazz album collection with Coltrane's "My Favorite Things" (it gets a lot weirder from there), but I'd also say that the most important characteristic of jazz--whether bebop, modal, or avant-garde--is group improvisation. It's completely at odds with the mindset of a metal band.
When a jazz band plays, everyone is improvising along with the soloist. A rock/metal solo is basically 16 bars of "look what I can do" over a static background. In jazz, the accompaniment is NOT background, and shifts and turns along with the soloist--a very high form of musical communication. And the soloist is creating a spontaneous composition, not simply showing off their skill set.
In some ways, Weather Report's early albums were the ultimate expression of this--the saying about them was that "everybody was soloing, but nobody was soloing." Some people find it murky and directionless, but once you "get it", albums like Sweetnighter and Mysterious Traveler are amazing.