Why was it dumb? Do you assume you would have been at ground zero? Because, if not, “duck and cover” could certainly save your life.
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If the shockwave from the blast didn’t kill you immediately, then there is the radiation poisoning. That and the total supply chain obliteration leading to starvation. But yeah, you might survive the initial blast if you’re more than 5 miles away.
The 50% casualty radius for the blast effects of even a 1 megaton airburst is about 2 miles. Even in a large-scale nuclear exchange, most people are unlikely to be that close to ground zero, and many people will not be at grave risk from fallout.
The people in charge in the ‘50s were a little more serious about the risks and saw plenty of reasons to keep kids from being needlessly injured or killed by falling debris.