Yes m7b5 chords are not confined to jazz--they're part of the vocab of diatonic harmony: they're all over the place. it's the chord you'll want to sing on the seventh degree of the scale. Don't blame jazz for the m7b5. Blame jazz for the Maj7#11, the "lydian chord."
Also 'm not advocating for the use of sevenths in Trad.
Also why do you disrespect polynesian culture that way?
A lot of folk music has an interesting indifference to chord structure. Lots of blues guys would go to the four chord whenever the felt like it, rather than at measure five, and it's often kind of relaxed about the momentum of origin and return.
I love this song:
https://www.youtube.com/watch?v=Sd0GnCtjgKE. I use it in class a lot because it's so indeterminate. The students don't know what to cal it; they don't know if he's black or white, they don't know what to think about the "quills," the panpipe. It's ot really going anywhere for most of the song even though its a song abut traveling. and then it gets to Chicago and ends.
I hear a lot of accompaniment to Irish music that just seems wrong to me, like the guitar player is trying to do I IV V or make it into a 1960s style folk song.
I was trying to discuss this with a friend who isn't any kind of musician, and I sent him this version of "the Rolling Wave," where I thought the guitar player was just coming at it from the wrong direction, trying to impose a harmonic structure that ended up making the tune less interesting and more trite. I have nothing against these guys and am sorry to hold them up as a bad example.
https://www.youtube.com/watch?v=wWOs_tl3TggOne of the things jazz musicians started doing in the 60s was "Quartal harmony" where instead of making chords by stacking thirds they started stacking fourths. A famous example is the piano on Coltrane's version of "my favorite things," especially the piano solo, starting at about 2:17
https://www.youtube.com/watch?v=qWG2dsXV5HIthere are whole classes done on that solo, and how relaxed it is and how it's not really interested in either leaving or returning (
https://www.youtube.com/watch?v=_kl9NBwii5w)
I think this is what DADGAD tuning is all about, subbing drones and root/five/octave for major and minor chords and to my ear, lending more of a "suspended" feeling and escaping the major minor alternation. This is suppose is what i mean about irish music being "modal." And I think thsi is why people hear someone like Dennis Cahill as being "jazzy."
Dont' worry, no need to be afraid of the spector of the seventh