A single nuke wouldn't be able to cause such widespread damage even if you were to poison a region of crops with the fallout. It would obviously be devastating, but nuclear weapons, whole huge, are still fairly isolated in the grand scheme of things. US dropped 2 on a single country in world war 2 and less than 50 years later the country was thriving. In order to cause widespread nuclear destruction, you'd need to wipe out multiple mega-metropolises around the world. And at that point, we'd all be much more fucked than the slavery status quo the world has been under since world war 2. You really think the group of people who have been controlling things for thousands of years aren't patient?