From a scientific perspective there is some indication that a nuclear war could deplete the earth's ozone layer or, less likely, could bring on a new Ice Age - but there is no suggestion that either the created order or mankind would be destroyed in the process.
A song must move the story ahead. A song must take the place of dialogue. If a song halts the show, pushes it back, stalls it, the audience won't buy it; they'll be unhappy.