The world avoided nuclear catastrophe in the last sixty years by a slim margin. So even if the Cold War reduced the murder count, it did so by ramping up the risk of human extinction.
But now consider the multiverse. The only logical way to square the fact that the universe is random--particles arbitrarily pick quantum positions--and also deterministic is to assume that every time a "random" event comes up, the universe splits and all possible events happen in different dimensions. Sure, we can't observe those other worlds, but the resulting theory is more elegant than the alternatives. Just believe this for a second.
To see how this fits in with nuclear war, consider a device which would blow up the entire world with probability 9/10. In nine worlds, everything is gone. In one world, cognitive scientists rave about how murder is so rare. In order to figure out the real decline in violence, we'd have to average across all worlds in which the Allied Powers win WWII with a nuclear bomb. Many of those worlds would destroy humanity entirely; but we are unlikely to be born in those worlds. The mere act of observing self-selects you into certain states; namely, those in which conscious, advanced life is possible, etc. etc. And 'bad events' like the use of nuclear weapons are much rarer in those worlds.
Put another way, it's not surprising that you're alive now, in the most populous period in human history. If you think that the act of "being a conscious human observer" is about random across all people, it's much more likely that you live in the 21st century than any previous century.
Somewhat surprisingly, observing that one is alive now makes it less likely that humanity will survive very long. If humanity were to survive for thousands of years, and spin off untold trillions of souls, it would be unimaginably unlikely to be born at a time when the population was (comparatively) trifflingly small. It's possible, though, that this could happen. Plato, if he made the same calculation, would conclude that humanity would be extremely unlikely to grow to its present level. But we're not Plato; and our best estimate of the duration of humanity is not very long.