> on a global scale, multi-state governance based on mechanisms like the UN, the international criminal court etc should be the mechanism for global governance.

The UN is not for “global governance”, it is to prevent the nuclear holocaust that would be WWIII by giving super powers a place to resolve conflicts. The international court at the Hague is only able to try war criminals, for example from the Yugoslav Wars, because the countries were not powerful enough to just ignore it. Just because we were able to try and convict Slobodan Milošević, doesn’t mean that China or Russia would ever extradite a former head of state for trial.