Without nukes, powers would confront each other in their own territories, leading to huge death tolls and devastation that were the hallmark of WWI and II.
Post nukes, conflict has been confined to the fringes of the world. Korea, Afghanistan (the Soviet-era fight), Vietnam -- these happened because the USA and the USSR deemed chose to fight it out over a piece of land no one cared _that_ much about, so that a loss could be accepted without 'going nuclear'. While it sucked if you were a citizen of these countries, the fact of the matter is that a war between the USA and USSR directly would have been much, much worse.
> Correlation does not equal causation
Wars between powers occurred fairly frequently throughout the last one thousand years. Post-nukes, they've stopped fighting each other _directly_. Most recent case: India v Pakistan -- 3 shooting wars in 24 years. Post-nukes: nothing, despite plenty of provocation. You keep looking for correlation coefficients. In the world of international relations, this is a bloody miracle and we'll take it.
> Like the peace that has been or is being kept in Korea, Vietnam, Iran, and Afghanistan?
This is the engineer's disease: all or nothing. There is and will be no perfect peace. The question is, are we better off keeping conflict on the sidelines rather than in major world capitals? Again, from a international relations perspective, yes!
Also, note that as countries like Vietnam and (South) Korea join the global 'core', it becomes increasingly unacceptable for them to be embroiled in conflict. You simply wouldn't have a Vietnam War or Korea War today.