Then that's not "political intercourse." I understand that war is not actually used as described in the quote. Which is the point. These military ideas of war are romantic fantasies.
Although I'm sure the victims of all the holocausts in human history will be heartened to know that it was just politics by a different means.
The full phrase is "the political intercourse of Governments and nations" [1].
Clausewitz's point is that if "such intercourse is broken off by war, and that a totally different state of things ensues, subject to no laws but its own," then not only does international law become irrelevant, but diplomatic resolutions to war impossible. Rejecting that war is a continuation of politics underwrites atrocity. (If war only happens as a last resort, and you are at war, it follows that you've exhasuted all non-military avenues to ending the war.)
> These military ideas of war are romantic fantasies
Clausewitz wasn't a military romanticist. To the extent here are romantic ideals at play, it's in pretending war isn't a continuation of politics.
> I'm sure the victims of all the holocausts in human history will be heartened
Why is this relevant to the correctness of the theory? Should we reject the heat-death hypothsis because it's uncomfortable?
I've already argued why rejecting war as a continuation of politics rejects diplomacy as a way to end wars. The Third Reich is a good demonstrator for why rejecting the political component of war is dangerous on the other end. Appeasing Hitler makes sense if parties will only pursue war as a last resort. Acknowledging his political interests, on the other hand, would have shown why--in that case--appeasement was destabilising.
Although I'm sure the victims of all the holocausts in human history will be heartened to know that it was just politics by a different means.