One thing that bothers me, but never seems to be addressed or considered by anyone, is the CO-EXISTENCE of nuclear weapons and nuclear power plants.

Surely, in the event of a war, you take out the enemy's power plants(?)
But what happens if you nuke a nuclear power plant? What happens if you nuke 50 or a 100? My guess is that you spread large quantities of dozens of extremely noxious radio-isotopes, some with extremely long half-lives, over most of the planet - making it uninhabitable - bye, bye human race!