It occurred to me recently while reading some literature on international affairs game theory that it's heavily in a state's interest to eliminate rivals while they're still weak.
Since there were absolutely zero credible state-vs-state security threats to America after she developed nuclear bombs, why did America not take the initiative and immediately crush any opposing nuclear programs? A bomb or two on the USSR, severe and credible threats against other Western countries (striking investment funds, blocking food supplies, etc.), and other nuclear programs would have instantly stopped, no? America would have had instantaneous control of global policy at the interstate level.
Instead, America let its rivals become enormous security risks. Why? I just don't understand the lack of foresight here--especially since the US Senate, state legislatures, and American nuclear scientists all immediately petitioned Truman to establish a global federation to prevent a nuclear standoff. It's not like the country wasn't warned.
First, history is not Civilization V. You can't just go and kill millions of people for no reason other than the naked pursuit of power. Whatever flaws Truman had, and certainly granted that the US has pursued neo-imperial policies, there's still at least the appearance if not the reality of a basic morality that respects human life. Unprovoked nuclear attacks are simply out of the question.
Second, and carrying on from this, if the United States DID pursue such a course of action, it wouldn't work out as you wish. Nuclear weapons don't give you instantaneous control of global policy at all; after all, how do you actually enforce things? It would instantly generate opposition to the US from every corner of the globe, and unless America planned to rule with an iron first, lobbing nuclear bombs at any enemies that emerged, whatever domination they possessed would evaporate rapidly.
In the end, rule does not happen through coercion alone. There has to be an element of consent, and the US (and the West generally) have pursued a policy of global domination through the "consent" generated by the market. That's why, despite losing their empires, Europe, and the G7 have managed to stay wealthy and more or less the dominant forces in the world.
The US nuclear weapons program was very slow to grow. It took until around 1950 until they had a sizable arsenal (e.g. a few hundred bombs), and those were all still very crude weapons that had to be delivered by long-range bombers. You cannot take out a state the size of the USSR with one or two World War II-style bombs — their industry and military and political infrastructure is large and dispersed. They would have invaded Europe as a result and reduced the American ability to strike them again (B-29s have very limited range).
Having nuclear weapons does not allow one to operate with impunity, either, even without some form of deterrence. One needs allies. In the US case, being able to have nuclear weapons abroad required being allowed to use military bases on foreign soil. If the Europeans thought that the US was throwing too much weight around, they could have revoked this ability.
Could the US have decided to go on a path of total world domination? First, you need a much larger number of nuclear weapons to do that, if you think they are going to be the lynchpin. Second, bombing generally does not win wars — boots on the ground does. The US lacks the boots to project power over the entire world in that way. Third, the last time someone tried to take over a huge chunk of the war with military force, it motivated the rest of the world to get together and destroy them. Not ideal. Fourth, it is extremely expensive to wage war, and wrecking the world economy is not going to help that. Fifth, in the a democracy you need some consent of the governed to wage a war, and the US populace would tire of a war of that scale rather quickly (they were already tied of World War II), even if they did think it was a good idea.
The reason the US chose the policy of "containment" with regards to the USSR was because ultimately that was the cheaper, more practical, and safer mode than trying to occupy huge areas of land and huge numbers of people by force, or to try and commit a genocide against them.