My dad said they would do air raid drills in elementary school (50's, 60's) due to the fear of a nuclear attack. They were taught to get under their desks.
I went to school during those decades. For us, it was listening to how bad drugs were (grouping in Marijuana with Heroin and the rest) by a police officer lecturing us (they called it DARE - DARE to keep kids off drugs.) I would have preferred duck and cover personally
I remember doing these. Air raid sirens would go off, we would dive under out desks, wait until teacher said we could get up. Sometimes we did drills to all march, in an orderly manner, out of the classroom into the basement of the classroom building, or to the locker rooms at the gym. IIRC during the Cuban missile crisis we got sent home early one or two days, but my memory is a bit fuzzy on that. This was in Bethesda, MD, adjacent to DC.
I've lived near Camp David and Site R for 50+ years, so we always joked that if the missiles ever started flying, we'd be the first to know and go.
Apparently getting under their desks was on the off-chance their school is far enough away to avoid being incinerated but still close enough for a pressure wave to blow out all the glass in the windows and turn it into projectiles.
The tradeoff is raising generations of children terrified of nukes destroying their world at any moment. Better safe than sorry, as you suggested, but it's not a zero cost strategy.
This came in handy when that meteor exploded over Chelyabinsk a few years ago. A teacher remembered the training and had everyone hide under desks, and they were spared laceration from the blown-in windows.
In Russia, this kind of training is not a long-gone relic - there's a class in school that's dedicated to survival in various situations, covering all kinds of stuff from emergency first aid to making shelter in the wilds. A subset of that is dealing with anthropogenic disasters, and a subset of that is civil defense. If I remember correctly, we had two hours covering nukes alone - likely targets in the vicinity, what kind of damage to expect where, how to build fallout shelters, when to evacuate etc. So far as I know, this all is still taught in schools there.
In Soviet times, the class was called "preliminary military training", and focused more on that aspect - not quite to the point where they'd shoot things, but it would involve timed field-stripping an AK, for example, and reading military topographic maps.
After 1991, the military aspects were stripped out, although in many schools they turned into an opt-in afterschool "patriot club" or some such. These were the primary source of videos like https://www.youtube.com/watch?v=LrxjYfl05ek.
Recently, they've announced that they'll be reviving the old Soviet format, so it'll become mandatory for all high schoolers again, beginning with the next school year (starting in September, 2023).
Everyone, especially in pseudo-intellectual circles like HN sneers at the whole "duck and cover" thing but any grade schooler can look a the concentric circles on a map and tell you that the area in which you'd best protect your noggin from the drop ceiling dropping a little more than designed is far greater than the area in which burns are a problem.
There was a brief, happy span of a couple decades without duck-n-cover or shooter drills, though.