Let’s say you commit a war crime. In order for your case to be heard by the court, you’d either have to:
Be extradited by your home country to the court. If your country does not acknowledge the validity of the court, that won’t happen.
Be kidnapped and shipped to the court. If your country does not acknowledge the validity of the court, then it becomes a hostage situation and an international incident.
International affairs don’t care about your preconceptions of law. ICE isn’t going to knock on your door to ship you off to the ICC and put you in the chiller. If you don’t agree to participate and you’re a major power like the US, you don’t participate.