The value of such precautions can be swiftly proven though the incredibly advanced technology of “looking at a map.”
Suppose a limited nuclear exchange results in Russia attacking New York City and detonating a 800-kt warhead, of the sort carried by an SS-25, right over Times Square. Obviously, if you happen to be buying a knockoff watch from a street vendor on the corner of 49th and Madison, or you’re in the audience watching “Hamilton,” you’re dead. Things are going to suck pretty bad for anyone in Manhattan as well as parts of New York City on either side of the river. But plug the effect into any number of online maps that morbidly show you the effects, and as you can plainly see, a lot of people - millions - could escape death or serious injury by taking cover. For much of the area simply being in cover will prevent any sort of injury. If you’re in Staten Island, or near JFK, being outside could cost you your eyesight and a lot of burns; being in cover will save you.
“Duck and cover” was not pointless during the era it was advocated – 1952. There were no usable ICBMs and the Soviet Union did not obtain over 50 nuclear weapons until after 1957. In 1952 a nuclear exchange would be a slowly-evolving bomber-based affair using a fairly limited number of small fission weapons. That was the era when ‘duck and cover’ was devised and promoted. It was a rational procedure in that era.
At some point of escalation, a world war (whether nuclear or otherwise) would cause complete societal breakdown. However that threshold was not reached in WWII, even though 50-55 million civilians were killed: World War II casualties - Wikipedia
It was not reached in the U.S. Civil War, which killed more Americans than all other wars combined, including World War I plus World War II.
An all-out nuclear exchange in 1988 would likely have killed much of the population in the US, USSR, Europe and China, and devastated the environment and sent whatever shreds of the world economy which survived back to the dark ages.
But no credible authority ever claimed that “duck and cover” would offer meaningful protection from a nuclear exchange involving 24,000 bombs.
Speaking of schools, they still advocate “duck and cover” from tornadoes – despite the fact that a direct hit by an EF5 tornado would level the building: https://benheb.github.io/tornado-days/images/1999-okc.jpg This is because most tornadoes are less severe and taking shelter increases chance of survival.
“Duck and cover” is still practical advice. Some significant fraction of the population is going to survive even an all out war. Many or most will die from subsequent radiation or collapse of civilization, but we generally view survival for as long as possible as being valuable.
There’s a large area around nuclear explosions in which you are unlikely to be killed by the blast and overpressure, but that you are in danger from severe burns or blindness from the nuclear flash and vulnerable to flying debris like broken windows.
Yes, if you’re at ground zero, then duck and cover won’t do anything. But it won’t matter - you won’t be alive long enough to feel stupid for ducking and covering. But a few miles away? It very well could save your life.
I don’t understand why people are saying that it’s somehow invalid now. What else are you going to do? If it increases your chance of survival slightly, or results in less chance of burns or blindness, why not do it? What else are you going to do? It’s practical advice.
A note about radiation dosage/exposure units: Older sources use Rads and Rems; Rads are an objective measure of radiation energy and Rems (“Radiation Equivalent Man”) are a qualified measure of the biological effect of radiation exposure. Other than for exotic radiation sources like neutrons or cosmic rays, they can usually be taken as equal RAD=REM. Newer sources use SI units of Grays (=100 Rads) and Sieverts (=100 Rem). IOW, a dangerous radiation exposure is hundreds of Rads or Rems but only single digit Grays or Sieverts.