"How can you possibly state that those songs would have 'vanished' if they hadn't been 'collected'...?"

They did do though, except for in a few isolated pockets. So its not supposition but a description of a process of extinction that actually took place with the arrival of modernity. Amongst the last people in the UK to keep alive the oral tradition were the travellers and with them the tradition died almost overnight with the introduction of portable tellies, or so I've read (c/f Jim Carroll).

If you want to explore this further can I recommend "Ask the Fellows Who Cut the Hay" by George Ewart Evans? It's a fascinating and beautifully written exploration of a rural community in East Anglia (where Evans lived at the time), written in the mid-fifties. His basic argument was that these communities had remained virtually unchanged from the middle ages to the end of the nineteenth century but that industrialisation, advances in communication, cheap travel etc had changed them beyond recognition in fifty-odd years. The elderly people he talked to (elderly in 1954!) he saw as the last remaining link to a bygone era. My suggestion is that the old singing traditions were part of this bygone era.