Why would anyone want to write "essaying popular songs"?

Because that's exactly what I saw, Richard - same as I see many Folksong Singers essaying Traditional Songs, or Bruce Mathiske essaying Caravan. Allow me to explain. Essaying would ordinarily (I suppose) be a matter of attempting something, or having a go. Here it's similar, but it's more a matter of acknowledging traditional continuance and the sort of aesthetic / cultural assumptions any non-traditional artist might make when approaching / covering a particular piece of traditional music to somehow make it their own, which of course it never is. I have somewhere my Caravan Collection which takes in everyone from The Mills Brothers to Martin Denny, but it sits squarely on the Tizol / Ellington original, the evolution of which was considerable between the initial recording of May 14th 1937*, and that which Ellington would record some 25 years later in a trio with Max Roach and Charles Mingus (Tizol's own versions notwithstanding). As musically accomplished as Bruce Mathiske's cover is, it is not part of the music / cultural lineage (tradition) that gave rise to the song**, thus I say essaying, because it ain't real in the way that the others are. Similarly, Buskers essay popular songs and Folksong Singers essay traditional ones - no matter how good they might be, they are not part of the original musical / cultural / traditional lineage as any Busker / Folksong Singer or Jazz Guitarist will be all too aware. One hopes.

* Sources differ as to when extactly this seminal session was, or who was leading - Ellington or Bigard.

** Song is used here in its Jazz sense, where all sorts of musical pieces and ideas are referred to as songs whether they involve words or not (and a Chorus in Jazz is very difference to a Chorus in folk). Although there are words to Caravan, and several iconic performances (Ella not least) the piece is more often than not essayed instrumentally, even by The Mills Brothers, who used their voices (in this instance) to imitate an instrumental ensemble with trombone and wow-trumpet solos complete with cheeky sycopations, but the only real instrument is the guitar backing:

http://www.youtube.com/watch?v=MJOs8roE94E

*

Why would anyone refuse to see that there is a difference of type, not style, between a folk art and a contemporary one?

Because not all of us are suckered into the prescriptive fantasies of the Folksong Revival. The very notion of Folk Art is so much patronising paternalistic hokum - it exists to suppress & disempower the very essence of working-class creativity that gave rise to the old songs & ballads in the first place.