Staying away from the International Criminal Court (ICC) was the right thing to do. The ICC is an independent court composed of international jurists with universal jurisdiction over war crimes, etc.
Not a bad idea in concept, but the problem is that its independence also makes it unaccountable, there are no checks or balances. It does not answer to the UN or the Security Council or any other body.
It is supposed to defer to nations that conduct their own investigations, trials, etc; but the ICC can claim jurisdiction at any point if they themselves determine that an investigation came to the wrong conclusion, the trial was unfair, or the sentence inappopriate.
That is the crux of the problem with this court for the USA. Obviously there are people on the international legal scene who harbor substantial anti-Americanism or whose ideology is hostile to American principles or who may disagree with an American foreign policy decision. Many of these people will be on the ICC and doubtless some would use the authority invested in the ICC to pursue their anti-American agenda.
Verdicts should be based purley on the evidence at hand.
No evidence, no trial. Bad evidence, then equit. Good evidence, then confict and you pay the price, no matter what your position in live, government, military, civilian.
I am not saying that this is the best court, we will have to wait and see, but on the other hand, when the last days do come, and we are all judged individually, no one will have a veto, so we better get used to it.