You are right, of course,
however, the Cold War was just an excuse for both countries to justify a bloated military budget while their own people starved on the street. Largely, the Cold War was propaganda courteousy of the military and media. It is very improbable that either the US of Soviets would have attacked each other. Instead they used it as an excuse to intervene in countries that were within their sphere of influence, destroying millions of lives in the process. It's sad to think of all the wasted human potential, all the time we spend building guns and bombs to kill other people (who just want the same things we do), when instead we could be composing pomes and operas, building temples open to peoples of all religions, and just practising normal human kindness.