I don't think I know anyone who believes songs rose unbidden from the ooze. (Booze, maybe.) So your first premise is lost. That they were altered and improved by anonymous contributors en-route to the current day, perhaps some will admit to that, although the "Folk Process" seems to be used in about the same circumstances as the "Folk Police", with only slightly better credibility.

I entirely agree that knowing the authorship would not add anything to the quality of a song, in musical terms. It may however have some effect on the historic value of the words.

Nah, I can appreciate the stuff without knowing how common it was, or wasn't, so your last premise falls flat too.