some of what you say is true,and while Jimmy rodgers used loius armstrong and Earl hines,and yodelled and used blues formats.
its not normally classified as JAZZ,in fact he is in the country music hall of fame.
I hear no modern jazz influence in the music ofLester Flatt EarlScruggs AND Bill monroe.
neither do I hear the influence of Ravi Shankar in the original Carter family,I do hear the influence of the blues,via Lesley Riddle.
Grandpa jones at least could entertain and while I prefer him marginally to Flatt and Scruggs.
they all pale into insignificance compared to Roscoe Holcomb Clarence Ashley ,Frank Profitt.