In a world where we have 9 nuclear powers, I struggle to see how your system would keep them in check; nuclear fallout effects all of humanity and quite literal

In a world where we have 9 nuclear powers, I struggle to see how your system would keep them in check; nuclear fallout effects all of humanity and quite literally could make the planet inhabitable. I bring this up because any system that replaces the current world order needs to be able to keep these nuclear powers in check.