But if you think that improvisation is as integral to trad folk as it is to jazz, I don't know what to say.

Once again it all depends what you mean by Trad Folk; on the UK Folk Revival Scene, from experience, I'd say it's pretty much anathema, although there's bound to be exceptions. In other parts of the world (especially where improvisation is integral to their classical musics) then you'll find improvisation in their folk traditions, though once again there's bound to be exceptions, often down to individual preference.