I'm late to the thread but....

"In my humble opinion I regard jazz, particularly trad, as part of folk music. "

*deep sigh*...You can't just 'regard' something like that and make it so. There is a REASON why there are different names. And, there are festivals especially for jazz.
I like jazz...a lot. I listen to it often, but just because a few jazz musicians have used some folk melodies to improvise on, that doesn't lump the categories together. They are WAY different approaches to music. The word 'trad' (traditional) can be applied to almost any music. I'm sure those who like Punk Rock could point you to 'trad' versions....