From the perspective of anyone concerned with limiting state power and preserving human life, the current arrangement of nuclear-armed governments is a disaster waiting to happen. As of this writing, nine governments (United States, Russia, China, France, United Kingdom, India, Israel, Pakistan, and North Korea) possess a total of 15,650 warheads, 4,300 of which are ready for immediate use. These governments spent $91 billion on nuclear weapons in 2010, rising to $104.9 billion in 2011. It may seem that only a madman would want even more of this, but there is a case to be made that nuclear proliferation among governments, even if it is not ideal from a libertarian perspective, is significantly better on libertarian grounds than the current state of affairs.
The first thing to note is that no nuclear-armed government has had its territory invaded by another government. While this is not an a priori truth, it is in agreement with all empirical evidence and the rational self-interest of rulers. Before nuclear weapons were invented, rulers could invade other countries with little chance of being personally affected by the violence. When only the United States had nuclear weapons, Truman was able to use them against Hiroshima and Nagasaki with impunity. But once the Soviets exploded RDS-1 on August 29, 1949, the monopoly on nuclear capability was lost, never to be regained. The advent of mutually assured destruction meant that anyone who dared to use nuclear weapons could expect to be hit with them in return in a matter of hours (minutes with modern delivery systems). While the ruling classes used the funds they extorted from their populations to build shelters to survive a nuclear exchange, they knew that such survival would not truly be life; they would have no useful territory to control and no people to rule upon emerging from their bunkers. As such, the creation of nuclear weapons has led to a more peaceful world, at least in terms of major wars between world powers. One may speculate that the acquisition of nuclear weapons by more governments (or private defense agencies in stateless societies) would take all-out warfare off the table for them as well.
Another benefit is that with a nuclear deterrent making an invasion far less likely, a government can afford to spend less resources on maintaining conventional military forces, thus freeing up money to either be spent domestically or left in the pockets of citizens to boost the private sector. (Of course, this does not mean that they will, only that they can.) For example, the United States has generally lowered its military budget as a percent of GDP since nuclear weapons were invented, with a few exceptions for wars. This also means that agents of bureaucracy as well as special interest groups within the military-industrial complex will be smaller, less wealthy, and less able to influence politics than they otherwise would be (though they can still be terribly powerful in some cases). Reducing the size and scope of government militaries and their equipment providers would obviously be good for pragmatic libertarian concerns about state power.
In an anarcho-capitalist world, it may be the case that nuclear weapons are completely absent. There are many libertarians who doubt that a libertarian society could square the use of nuclear weapons with libertarian principles, as killing innocent bystanders is impermissible under the non-aggression principle. Only by viewing those in the vicinity of the blast as human shields and applying the theory of negative homesteading could the use of nuclear weapons be justified in libertarian theory. But an idyllic Ancapistan is still out of reach, and no method for getting from here to there has been effectively demonstrated. As such, we must deal with the world that is and is likely to be in the near future, not the world we want.
As for the world that is likely to be in the near future, the transition from statism to anarcho-capitalism will almost certainly not occur overnight. There is almost certainly going to be a period of time in which some parts of the world still have governments while other parts of the world are anarchist control zones, regardless of the means used to circumvent or abolish existing states. When this happens, the stateless people will have economic advantages over those who live under the burden of government regulation. Eventually, this will lead to conflict as rulers blame the anarcho-capitalists for luring away people and resources that governments need to continue functioning. States in this time period will be dealing with an existential threat of a sort that they have not faced in time memorial and to which they have no answers other than to abolish themselves or use violence. Those in power who are unwilling to give up violent dominion and live peacefully with their fellow human beings could consider this situation worthy of using nuclear weapons, and if the anarcho-capitalists want to be able to defend themselves, they will ultimately need a nuclear deterrent. Nuclear proliferation serves libertarian interests in this scenario as well, as it means that there will be more potential sources from which the anarcho-capitalists can acquire a nuclear deterrent.
Of course, any decent philosophical case must deal with potential objections.
Nuclear weapons can turn rogue states into dangerous threats. Just as nuclear weapons can reduce the belligerence of world powers, they can also protect rogue rulers from being overthrown, thereby making them more willing to threaten their neighbors. This argument is not credible due to the number of counterexamples. Leaders who seek nuclear weapons are portrayed by the media as insane, but their behavior demonstrates rational self-interest and skilled use of brinkmanship. While they are by no means benign, they do not have a track record of acting like madmen. Even Hitler refused to use chemical weapons (the closest analogue of a nuclear device in his time) on the battlefield in World War II due to fears of retaliation as well as first-hand experience.
Just because mutually assured destruction has worked in the past does not mean it will work in the future. This is true, but when all empirical evidence as well as the rational self-interest of influential people points in one direction, it is wise to go in that direction until contrary evidence is available. To argue that this does not apply here is both a special pleading fallacy and an appeal to fear. That being said, a military commander’s strategy in a conflict between nuclear powers might be a first-use of nuclear weapons, with the hope of destroying the other side’s nuclear arsenal before it can be used in a counterattack. If this were to happen, millions of lives may be lost in the two countries in such a war. But consider the likely events that would follow. The rest of the world would be shown first-hand how devastating nuclear weapons are, leading to much less willingness by other rulers to initiate their use. Also note that should the person or people who ordered the first strike survive, they would be the most wanted criminals in human history, likely to have very high bounties placed on their heads by other governments and private individuals all over the world.
Nuclear weapons are too dangerous to be owned by individuals. But how will they be banned? We can see how well bans on other types of weapons have worked. Like gun control laws, the scribbles of politicians (or the terms of dispute resolution organization contracts in a stateless society) saying that civilians must not possess nuclear weapons are not of concern to a misanthrope who wants to hold a community hostage (or just perform a massive murder-suicide). There is also the matter that enforcement could not reasonably lead to an armed confrontation, as a surrounded psychopath in possession of a nuclear device will most likely detonate it, blowing up several square kilometers and everyone in them. Furthermore, other weapons of mass destruction have been more widely available for longer than nuclear weapons have, and they go all but unused by criminals because they can achieve their goals more easily with other means. After all, why use chlorine gas or nukes to kill people when crashing a plane or shooting up a museum is easier? Finally, one must note that while private individuals have never used nuclear weapons despite the fact that there are probably some that have been lost by governments available somewhere, governments have used them, so which is the greater danger?
More nuclear powers means more opportunities for terrorists to get and use nuclear weapons. Terrorist groups operate outside the control of governments, and governments have a poor track record of predicting the behavior of terrorists. The possibility of being hoisted by one’s own petard, the high risk of being found out, and the high cost of building nuclear weapons mean that governments have every reason not to provide nuclear weapons to terrorists. The potential for terrorists to take nuclear weapons from governments has been dealt with in the previous argument.
To conclude, this is not an ironclad libertarian case in favor of nuclear proliferation, but it will suffice to start discussion on what is certainly an important topic.