The Cold War has several peaks and valleys in terms of "salience" of nuclear war as a threat. The late 1950s through the Cuban Missile Crisis was one such peak — clear fear that this was something that could and might actually happen. Then you see a gradual lull through the detente period, until the late 1970s. Then things start to ramp up again, coming to a new peak under the Reagan administration in 1983, where nuclear war seemed almost imminent. Then as the Cold War starts to cool down again, an easing off, that becomes a dramatic "cliff" after the dissolution of the Soviet Union in 1991.

It's not a coincidence that during the "peaks" you start to see a lot of "nuclear war media" produced, whether it is On the Beach in the late 1950s, Dr. Strangelove in the early 1960s, or War Games and The Day After in the the early 1980s.

Something like American Pie is, in its nostalgic way, talking about the early 1960s (when fallout shelters were, briefly, a cultural "thing").

Cultural products are both products of, and contributors to, the zeitgeist, the general collective consciousness and awareness we all share. So it is not surprising that you see fewer prominent contributions at times when that zeitgeist has shifted to something else. It is not that they do not exist (I am sure, if you looked, you could find 1970s rock references to nuclear war), but that they did not become popular, and thus were not incentivized. (You could write a song about nuclear war today, but it wouldn't have a chance at getting into the top 10. Whereas a song about our present anxieties — like climate change — potentially could.)

Anyway, the best single book on the changing attitudes and fears about nuclear everything (war, power, etc.) is Spencer Weart's Nuclear Fear: A History of Images (1988).