I have my doubts that any nation is going to accept the precedent that other nations can have authority over their use of military force.

That also sets a difficult precedent, both for soldiers and the court. If following an order to participate in an invasion of another country, while only engaging with valid military targets according to the rules of war, is a war crime if the international community later decides it wasn’t justified then soldiers will become war criminals not because of their actions being brutal or unethical, but because they were insufficiently aware of the global opinion of a war.

Second, it potentially puts the court in a position where they suddenly need to imprison literally hundreds of thousands of soldiers, to say nothing of arresting and trying them. This could easily make the court appear toothless when they fail to have the power to arrest the US army, nor to actually have a place to put them.