It's one thing to be bent on world domination, and quite another to have the ability to carry it out. Back in 1944, it was an option. Today, with nukes on the table, it's not. What do you think keeps crime in check - the police? Criminals are much more afraid of being shot and killed by an armed citizen than being caught by the cops. The same thing applies to nations, which is why there will never be a major conflict between nuclear powers unless one side's nuclear deterrence is rendered impotent first.
The math works like this:
1. If I have nukes, and you don't, I get to do whatever I want to you - invade your country, take your resources, whatever. This is the preferred state for me - and I will do everything in my power to maintain it.
2. If we both have nukes, I can't win a major conflict with you, so there's no point in starting one. If I attack you with conventional forces, you'll counter with nuclear strikes once you start losing. I don't like this scenario because I can't impose my will on you, but instead have to treat you as an equal, whether I like it or not.
BTW, political leaders dislike nukes because it takes some of their options away. Oil prices to high? Let's go take someone elses...oh, drat, they have a nuclear deterrent. The military-industrial complex dislike nukes because they're bad for business - who need's trillions of dollars in soldiers, tanks, aircraft, and warships when a few hundred nukes will provide all the security you need? Of course, that also rules out all that nation-building stuff that every empire wants to do...
In any event, we'll know the answer in a few more decades. Nuclear technology is 70 years old now - it's only a matter of time before it's widespread. What happens after that will be...interesting.