Plus, as bad as radioactive incidents can be, they don't affect the climate. Once the radiation dies down or is mitigated through clean-up efforts there will be no lasting impact on the world. In other words, with the right insurance policy you can recover from a disaster.

Hiroshima and Nagasakia were both deliberately targeted by nuclear weapons and are still inhabited. Cleaning up the mess can be expensive, but it's not impossible.

Cleaning up the mess made by a coal plant is basically impossible, the effects are too far reaching.

Seriously? "Expensive but not impossible"?

I'd take a contaminated room any day over a whole planet slowly cooking itself to death.

Yeah, because technology advances magically if you will it enough...

Thus it builds up in our ground water and atmosphere with no warnings and little community notification.

To be clear, my suggestion would be to google "category error".