False. Global solutions can come from decentralized market forces if you don’t have corruption hijacking the effort. All countries, except the US are on board and would arguably be moving faster and more aggressively if the US were leading rather than sabotaging efforts. Governments rightful role, whether its local, regional, national, or global is to set the rules of markets so that their natural forces move for an efficient and utility creating end. The market may demand child labor but government on any scale rightly intercedes to short circuit the market drive because it destroys utility (happiness or wellbeing) of the children and, in the long term, society as a whole as the population is less educated, healthy, and equal.
Further, I’d actually argue that most individual autonomy is stripped at the local level. You’re homeowners association can do more to rob you of individual liberty as the UN. In fact, I’d argue the global institutions, in some meaningful ways, have been the biggest drivers of restoring individual liberty. You might not feel it if you live in a market driven democracy; but the facts of development over the last 80 years, the increase liberty globally speak for themselves.