Here's a thought-provoking piece on how nuclear power problems scare us more than they should. Maybe we just can't stand the idea of death via invisible radiation? But the point is, we need power, and if we swap nuclear for something else, that doesn't make us safer.
I think the easiest way to imagine this is to think of a dam. If a tsunami or earthquake busts a dam, thousands are likely to be killed. Meanwhile, go coal and people die from it every day.