As for playing "all kinds of crap". I think that this is something that many people overlook. Many performers in all fields of 'folk' music that I am familiar with play all sorts of material eg; Charlie Patton's attempt at "Running Wild", Skip James "So Tired" (I'm so Glad), Bill Broonzy "Shanty in old Shanty Town" etc etc etc. I once spent an evening with Buddy Guy playing around on an acoustic guitar when he went into "You Are My Sunshine" plus other later pop numbers and I still have the tapes to prove it.
Most musicians will play and enjoy many types of music but when it come to making your living - or attempting to make your living, you have to play what the customer wants or what you perceive that he wants.
I'm sure that the Carter Family may have a chosen an even wider range of material to record if Ralph Peer hadn't insisted that the material should all be non copyright in order that he could publish it. Likewise any black musician that played a guitar became a 'Blues Singer' when blues was being marketed. Broonzy reverted to playing acoustically when the European audience discovered him because that's what they wanted to hear and he did a great job and put on a great performance. Sadly he still gets some flak for giving the public what they wanted. Some writers still accuse him of 'going commercial' and even adopting overalls during his stage appearances, personally I believe this to be bullshit. Did anyone ever witness this??? I know there is a photograph of him with a mop and bucket but I believe this to be a publicity shot for his track "Moppers Blues". Whenever I saw him he was always dressed sharp as a tack.
Sorry Folks I digressed but Big Bill was one of my first heroes. My whole point is Leadbelly wasn't a blues singer, but he incorporated blues in his repertoire and I suspect that many other 'blues' musicians were the same.