Uhhhhh, Violinia....
This can't be at all healthy... I keep agreeing with you! What's going on?!
Seriously, I can't understand how someone who doesn't actually play some jazz can hope to teach it. I mean, you
feel it, not just transfer printed music to whatever instrument - the grand woohoo seems of growing popularity these days!
I'm not sure whether it's quite the "you've either got it or you haven't" syndrome because I believe we all have rhythm, we all (hopefully) have emotions and
some sensuality but it doesn't mean that people can necessarily tap into these things or develop the aural and technical wherewithall to be able to use what they find.
It would seem that you have to take your ability at chord/harmony recognition and/or replication for granted so you can 'compose on the fly' even if you are effectively creating variations - and this doesn't seem to be in the normal "classical" curriculum.
So, right, AB classical teachers ought really to get out there and do some gigs before attempting to teach jazz. I would rate the chances of learning to play jazz from a book about the same as I would learning about sex from a book, if I might be so bold...

R