North wrote:

If they don't get killed from the blasts, they will die soon after from
the radiation, and disease

All it takes is a believable threat of nuclear war to drive people out
of the cities, like just one city getting nuked. They'd be hitting the
stores and then break into homes before they'd resort to eating bugs and
strange plants.

Same goes for plants, they will all die and the land will turn into a
bearon waste land with nothing but death everywhere.

Radioactive fallout doesn't kill plants, it poisons them.