That's an arbitrary statement to make ("I believe international treaties and bodies should exist, but make an exception for criminal courts"). I believe that criminal courts should matter even more than non-criminal courts such as the UNCLOS' court, mostly because even centuries ago, treaties related to war crimes have always been seen as a bigger priority for most empires and nations than other types of treaties have been. The ICC is our best way to enforce treaties like the Geneva Conventions.

The ICC is overwhelmingly popular with most countries and people, most people who oppose it are those from countries which harbor war criminals and try to make their opposition look like it stems from legal issues with international jurisdiction, and not the truth which is to protect their country's ability to commit war crimes unabated.