"blocky and ungainly' indeed and in most cases oral tradition has improved on this. "
You cannot possibly prove which way around this happened and it is ingenuous to suggest that you can
There were many broadsides sold but very few if any examples of them being sung widely - by Roud's description, it was an Urban occupation anyway.
The proof of the pudding is in the eating - look in Bagford or Roxborough or Ashton or Ensworth or Euing or Hindley.... they are overwhelmingly bad songs - that's why their authors fully earned the derogatory title of "hacks"
You may as well claim that William McGonagall wrote the Child Ballads.
Jim Carroll