There are two different view point on military strategy. One is that of a warrior, whose ultimate purpose is to win a glorious victory in a war. Certain warrior mores and mentality find their ways into their strategy. Its objective is to set up a one great victorious war.
On the other hand, the other is that of a ruler, who rules over his domain. In this case, it matters less on how glorious the win is as long as his army wins. He does not have to win a war if he can do it in other means. Or avoid it and still prevail. In this point of view, military strategy becomes combination of intelligence, sabotage, PsyOp, geopolitics, management of war materials, and actual fighting strategy itself. Sun-Tzu belongs to this group. His strategy is to deliver a (not necessarily military) victory in most efficient manner, which sometimes is not compatible to warrior ethos.
I am not sure where I should place Clausewicz. He is between the these two poles, leaning closer to warrior ethos according to my guess.
I would have to agree with all of what you said. I think that Clausewitz was trying to show both the military types who were all about the military ethos, and politicos, who wanted to achieve political victory by any means, that both had their part to play in the drama of national conflict. That both must be taken into account by both the military and political leadership, working together, to achieve national ends. And to achieve them with minimal military and political cost.