Believe it or not, right now the US has a tremendous first strike advantage over both Russia and China. And they know it. The Russians and the Chinese are working to overcome this advantage, but they haven't been able to for over 60 years and it is doubtful they will be able to, unless they utilize space and the moon. WMD's on the moon would be intended to take away the US first strike capability and preclude the use of nuclear weapons by the US.
Chinese don’t need nukes on the moon. They can send multiton projectiles of lunar matter from low lunar gravitý to hit targets on earth with kinetic strikes more powerful than the largest H-bomb. Review the death of the dinosaurs...