viz., "a supra-national entity that has laws, courts and the means to enforce the peace."
RedLogix 1.1.1.1.1.1
In my view that while the ICC was undeniably a good idea, it never attained the commitment across the board to permit it to succeed.
I'll go back to my original parallel; the reason why nation states are mostly lawful and peaceful places is that ordinary citizens forgo the right to coercion and revenge and place it solely in the hands of the nation state.
In the case of the ICC that never really happened; while most nations signed up to the ICC, there was never the necessary commitment to cede the nation state's own authority and interests. And while I agree the USA is the most outstanding culprit in this respect, it's also understandable given that as by far the most powerful sovereign nation it had the most at stake.