On the other hand these black swan events usually aren't that bad. For instance the Fukushima disaster, without an evacuation, wouldn't have killed any more people than a equivalently sized coal plant operating in the same place for as long as Fukushima had operated. The difference is just that with Fukushima the deaths are relatively concentrated in time.

Now, Chernobyl was a disaster you're not going to see with the normal operation of any class of power plant. But hydroelectric dams also have the potential and sometimes do fail in ways that kill thousands of people but I don't usually hear people oppose those power plants on these grounds.

I think that the real reason people have such a fear of nuclear power plants is that we use the same terms, "radiation" and "fallout," for the dangers from a nuclear reactor failure and a nuclear war when the magnitudes are as different as a pebble and a boulder. I grew up mostly after the Cold War and always associated those terms with nuclear power and never realized that if you're a hundred kilometers downwind of a megaton scale groundburst you can die puking your guts out from fallout a couple of hours later.