Getting back to the original question

...Is it right to lump the writers into folk?..

Well of course it isn't. I am a singer of folk songs and also a singer/songwriter.

Naturally, because of my folk singing background, some of my songs are based on folk themes or are deliberately stolen from my folk song repertoire.

My own songs could be classified as Novelty, Bawdy, Social Comment, Country, and Love Songs.

I imagine that many singer/songwriters have similar diversity among their works.

So if you group Singer/songwriters into a category of their own, you would probably find that the most consistent feature of the group would be 'variety'