Fallout is used in nuclear war to limit troop movements and other purposes. Making an area a no go zone is exactly one strategy.

A very real danger is a nuclear power that has a deranged person in charge. They know they don't have much time left, they don't care what happens after they are gone, they decide to fire off all their nukes.

https://en.wikipedia.org/wiki/Apr%C3%A8s_moi,_le_d%C3%A9luge

Chernobyl had tonnes of radioactive material, a nuclear bomb has much less material, in the kilograms. After Chernobyl blew its lid off, the reactor core was laid open. Witnesses said they could see a beam of light going into the sky. It was the radiation ionizing the air. A helicopter that was trying to drop sand onto the reactor accidently flew too close over it, giving the pilot a lethal dose.

Maybe not "accidentally". That pilot may have known the danger, and done it anyway. I seem to recall reading that he did, but I can't point you to a source.