I mostly agree. However, the de facto autonomy of the Great General Staff, arising out of the German government's defective makeup, was the deep problem. The constitution of the German Empire was fashioned by Bismarck to preserve monarchical power, i.e. his power as the Kaiser's chancellor, behind a facade of democratic accountability. And that system worked well enough as long as Bismarck was operating it. In his day, no doubt, the invasion of Belgium, if proposed, would have been summarily rejected. But Bismarck's system without Bismarck proved dysfunctional, creating a power vacuum into which the Great General Staff stepped.
The German invasion of Belgium was one of the great strategic mistakes of the war.
A mistake that German civilians would rue in 1919 as they starved under the British blockade.
You mention that the general staff did not coordinate with the foreign office.
True.
But I don't think that it would have made a difference if they had coordinated.
Germans are naturally arrogant when they think that they are winning ("The Hun is either at your feet or at your throat." - Churchill).
That arrogance leads them to do things that thinking people would never consider. The Zimmermann telegram is a case in point.
(For a modern example, see German foreign minister Heiko Maas and his toadies sneering at Trump at the UN.)
German diplomacy is often what Thucydides described. The problem is that the Germans often misjudge their strength.
I mostly agree. However, the de facto autonomy of the Great General Staff, arising out of the German government's defective makeup, was the deep problem. The constitution of the German Empire was fashioned by Bismarck to preserve monarchical power, i.e. his power as the Kaiser's chancellor, behind a facade of democratic accountability. And that system worked well enough as long as Bismarck was operating it. In his day, no doubt, the invasion of Belgium, if proposed, would have been summarily rejected. But Bismarck's system without Bismarck proved dysfunctional, creating a power vacuum into which the Great General Staff stepped.