You are right about the proportion of songs issued on broadsides over all the centuries not making it into the oral tradition. BUT of the general corpus of songs referred to above I personally have copies on broadsides of about 95% of them, excluding obvious sub-genres, sea shanties, children's playground songs and rugby songs. Try me with say 20 titles, of well-known ones, not obscure LOCAL songs. This is before I start in on the sheet music.

Here are a few authors to be going on with:-

17thc
The Keeper..Joseph Martin

The Leather Bottle..John Wade

My true love I've lost; Famous Flower of Serving Men; The London Heiress....Laurence Price

Serving Man and Husbandman; The Baffled Knight (rewrite); The Gosport Tragedy; No, Sir, No; The Bold Grenadier...Richard Climsell

Die an Old Maid; John Appleby; Stormy winds do blow; O Dear O; Robin Hood (Child 154)...Martin Parker

The Spanish Lady's Love...Thomas Deloney

Big Rock Candy Mountain...Richard Pocock

Boys of Kilkenny...Thomas Lanfiere

Robin Hood and the Beggar; Johnny Armstrong; Robin Hood's Chase; Robin Hood and the Butcher..... Thomas Robins

18thc
Down in the Meadows...Thomas Wise

The Three Butchers....Paul Burgess

19thc
Caroline and her Young sailor Bold; The Rambling Soldier; The Gallant Female Sailor....John Morgan, wrote mainly for Catnach

Pretty Caroline; The Constant Farmer's Son; Flora the Lily of the West; Bonny Bunch of Roses....George Brown

Of course I can't prove any of this. These people were credited on the actual broadsides, and apart from John Morgan we know very little about any of them. I respect your opinion expressed above but I also have the right to disagree with it, based on many years' research. It is also the opinion of others who have spent many years researching the relationship between print and the oral tradition.