Despite the "balance of terror," why did people still fear nuclear war?

Soviet countries like Russia and US started to conduct a series of nuclear tests in order to create fears against each other.

Fear of nuclear explosion prevailed everywhere in US from 1950, that the schools in US issued special tags in order to recognize the corpse if any unforeseen explosion happened.

Bomb shelters and entrenchments beneath the building were constructed in case of assaults and bombings. Nuclear bomb drills were conducted which made people aware that they have to safeguard in case of explosions.

Nations with the economic resources and military might to dominate the globe