I said often, not always. Also, it tends to be an amalgam of different pasts. Like right now what the US is doing in the Middle East looks a whole lot like Athens during the Peloponnesian War, and what we're doing financially looks like what Japan did.
So, I do think it is an accurate phrase, but misunderstood.
Quite true, but classics focus on distilling principles. If the authors' thinking was valid then, there isn't any reason it shouldn't be valid now, as I've been arguing that at least parts of the past repeat.