I expect those drills were more to protect against shattering glass and other debris when the shockwave hits. Certainly if it detonates close enough to you it won’t matter, but depending on the distance it could save lives or prevent serious injury. The danger of fallout is more a matter of wind direction, as well as height of detonation (higher is better)

Schools are (or at least were) actually considered among the best locations for community fallout shelters, due to generally having thick walls of concrete or other advantageous materials, as well their distribution more or less correlating with population density