Not talking about INCLOS, if that's what you're referring to. Talking about the long-accepted notion of a country's sovereign airspace corresponding with the maritime definition of territorial waters as being 12 nautical miles (22.2 km) out from a nation's coastline. Airspace not within any country's territorial limit is considered international, analogous to the "high seas" in maritime law. ADIZs are not really codified in international law, but are constructs which allow a sovereign nation to establish airspace extensions in which the ready identification, location, and control of civil aircraft over land or water is required in the interest of national security. I think I've got that right, but I'm sure there's a JAG or two on the forum who will correct me if needed.
Agree on all, particularly the point you make that ADIZ boundaries are not based on territorial waters/national airspace.
Although it doesn't really have anything to do with ADIZ per se, the double irony is worth noting: The U.S., which has not ratified the international law limiting territorial waters/national airspace, conducts FONOPS to enforce the limits which China ignores, even though China HAS ratified said treaty. What was the saying? "Never start a [maritime] war in Asia." Something like that...