Interesting question, Spaw. I think of Jazz as easier somehow, because it's so very much more recent than "Folk". Sure, I know that jazz has its origins back in traditional music styles, but what most people think of as "Jazz" is a 20th century musical form that went through an incredible flowering and evolution in a relatively short period of time. Ellington is a reasonable choice (but not the only one) because his influence extends through much of this time period.

But how would you pick a single individual for Folk and Traditional music in even one country, given that the types of music that people consider "Folk" have been evolving for centuries? In the US, you'd be comparing apples and oranges if you try to decide on one person to represent all of these sub-categories of American "folk" (listing just a few off the top of my head...):
Anglo-American traditional song
African American blues and field hollers
Southern string band music
New England and Southern shape-note and gospel
Western ballads and cowboy songs
Ethnic musics from American immigrant communities, from Scots-Irish to tambouritza to salsa to polka to - well, you get the idea...
Work-life related songs of miners, lumbermen, sailors, etc
Community-based dance and social music like Zydeco, Conjunto, contradance, R&B, banghra, etc
Topical & political songs and broadsides (which have been around since English settlers first came to America and wanted to gripe about things...)
Commercial/traditional forms like bluegrass, Western swing, folk-pop Kingston Trio style, etc
and the dreaded Singer-songwriter Omphaloskeptics...

And, yes, I know that "Jazz" encompasses such divergent forms as Dixieland and Coltrane, but as a geneticist, I can tell you that pedigrees are a heck of a lot easier to trace over a small number of generations than over a long period of time, and that evolution of musical forms is similar to that of creatures, with new hybrids rising from cross-fertilization between different gene pools (except in Kansas, where God created all the types of music we see today on Saturday afternoon...)