lawyers cost money, and my impression anyway is that the legal position in England is actually far from clear. And then imagine a lawsuit over the respective ages of a published dance collection and a manuscript, both c 1750 (this is all purely hypothetical, I dont own old manuscripts, thought I do research them). And since the likely royalties from recording an old song or fiddle tune might be in pence rather than pounds, the full majesty of the bewigged judges and barristers would be a bit much, just to determine who had rights to the loot.
Let's put the question another way. Has any museum (or individual) ever tried to establish any rights in some music, just because it happened to own a book, published or manuscript?