Yes, we need to collectively do everything we can to prevent a nuclear tragedy of the commons. That includes continued disarmarment of countries already armed. The more devices exist in the world, the higher the probability that some will fall into the hands of people who are not subject to the same incentive structures as secular governments (i.e. religious nuts) who would eagerly use them. One nuke being unexpectedly detonated in a major city could easily escalate into world-ending catastrophy.

This is never going to happen because the current nuclear powers keep abusing their power to benefit themselves. Look at Ukraine. They were effectively invaded and part of their territory annexed. There is nothing that can be done because Russia is a nuclear power. Or look at Libya or Iraq or Afghanistan. All of these invasions are backed by the threat of nuclear weapons.

It's not even too much to say that the only really sovereign countries are countries with nuclear capabilities or the ability to acquire them very quickly.

Why do people throw term "tragedy of commons" at every problem involving group? This issue has nothing to do with "tragedy of commons" which deals with exhaustible resources, not nuclear weaponry control.

Also, as I remember US bombed major cities using nuclear bombs, world didn't end.

The moment after the US bombed Nagasaki, there were no more usable nucler weapons left in the world. There was no such thing as an ICBM. Right now most of the world is pre-targeted by thousands of nukes mounted to space vehicles spread across half a dozen countries and on strike submarines. In the modern era if a country believes it may be under nuclear attack by another nuclear power, they have less than 2 minutes to decide whether to launch because their retaliatory capability would be crushed after that point. There is nothing remotely comparable about nukes in the ww2 era vs the post cold war era.