That’s one strategy. Another, once the nuclear cat is out of the bag, is mutual assured destruction (MAD). If that’s your strategy then it is hypocritical because then the point is that everyone has enough power to destroy everyone else so no one will make a move.
I personally think that both strategies are stupid. The former will just breed current and future resentment and the latter is vulnerable to one unstable person with authority to use the weapons.
But I don’t have any sort of alternative so it seems like preventing others from getting nukes and then falling back to MAD is just the way the world is working.
Alliance networks are what gave us WW1.
The point is that the reason given is to protect the free world, when it is doing anything but. It’s just keeping the same people comfortably in power, capable of stepping on their enemies at will.