The fact that we are alive seems to demonstrate precisely the opposite. You also conveniently forgot how many countries engaged in bilateral disarming programs (well, maybe Ukraine shouldn't have...) and how it generally makes sense because these nuclear weapons are expansive to maintain.
Still, you consider global atomic war a recurring risk every year, because you do not trust fellow human beings taking the right decision: "we can't be trusted".
This is why I believe this opposition comes from wrapped world views, a lack of trust in the future and future generations.
It seems like a sad way to live. Meanwhile, the world is improving, little by little.