To be sure, the reasons for their vanishing are a little inconsistent. Indeed, in the books, we get the flat out statement that burning witches was useless because they could magically protect themselves, though other statements make clear it's not so perfect. And there's the little aspect that if wizards can magically cure things Muggles can't, it's hardly insane to want them to do it and resent it when they refuse, and that when your children can accidentally injure or even kill others with wayward magic, strong reactions are inevitable.
However, one thing it does perfectly is grasp that it would be an never-ending battle. People being people, even fearful persecution will not keep them from making contact forever. (Especially not when the persecution is in the past.) Arthur Weasley and a number of other Ministry officials are endlessly covering up the practical jokers, the criminals, and the careless. (Using spells with abandon that would certainly be crimes in Muggle law if they were known.)
Though I was thinking about the fleeing Muggleborn in the seventh book -- one could easily imagine them forming yet another wizarding world, secret from Muggles and the purebloods. Imagine a world in which wizards endlessly splintered into more secrecy. . . .
(L. Jagi Lamplighter brushed on this in her Rachel Griffin books, though the reason is not political infighting.)
