Ah, but suppose it became clear old Bert had inserted the odd verse, or indeed made whole songs around, say, a discovered song title and got a taste for period songwriting.

Again, we don't need to speculate - we know that he did this, sometimes improving the song, sometimes buggering it up. You can imagine a kind of alternate Bert Lloyd who was an incredibly skilled ethnographic forger, with access to the Bodleian ballad collection and the ability to control Cecil Sharp's thoughts, but if you're going to do that you may as well imagine him with X-ray vision and leaping tall buildings at a single bound. Back in the real world, there are some cases where we can see what was trad. and what was Bert, and others where we can make a pretty good guess. It's history, not religion.

those who insist a song has qualities by the mere expedient of it being old

Who would those people be? There's a big difference between an old song that's been through the folk process and an old song that's been preserved unchanged - songs in Shakespeare's plays, for example.