Well, there are better ways to protect yourself in the event of an earthquake. But, that's not the point: we're talking about how earthquake drills were just rebadged nuclear attack drills.
Anyone who's ever been in an earthquake knows you ain't eating snacks if you're stuck under rubble. Also, school desks don't offer much protection from rubble either.
The point is the same. The drills never went away no matter where they were, and it was obvious what they were actually for because they didn't really address the catastrophe they were purported to be responding to.
It was mostly converted to "earthquake drills" by the '70s. The purpose changed as the Cold War fizzled out, but the drill itself never really changed.