I don't think any of them have claimed the throne since Bonnie Prince Charlie. And, yes, between the War of the Spanish Succession, the Great Northern War, unrest in Hungary, unrest in Catalunya, and Louis XIV being elderly by the standards of the time and having a young child as his heir, plus all the general messing about with bits of Italy and the Netherlands being swapped around, everyone had their own problems, as well as France agreeing to the Hanoverian succession as part of the terms of ending the war.
It is extraordinary, though, as you say. The current 56th in line to the throne is (thank you, Wikipedia!) Alexander Ogilvy. Imagine if he were suddenly declared to be the next heir. And at least he isn't a German prince who barely speaks a word of English.