No one (so far as I know) is claiming that it's obvious that taking more vacations (than is normal in the US) increases productivity; only that it's true. Your

No one (so far as I know) is claiming that it's obvious that taking more vacations (than is normal in the US) increases productivity; only that it's true. Your argument is entirely devoted to demonstrating that it's not obvious, and has nothing to say about whether it's true. (Is it true? I don't know, though it seems very plausible to me. It's certainly commonly said, and really not all that counterintuitive.)