Ding ding ding. This is always the caveat tucked away in nuclear discussions. "It will be fine, as long as everything is going fine." Things don't always go fine. When they don't go fine at a coal plant, things are bad, but they are recoverable; they can be cleaned up, and that land can be repurposed, even if its prior purpose is no longer feasible due to structural changes or pollution. There is no permanent, decades-long exclusion zone.

>I'd risk a %0.00001 chance of dying by cancer sooner living next to a nuclear plant vs. a 1.0% chance of dying in a road collision with a fuel tanker or a 0.05% chance of dying sooner with emphysema by living close to a coal-fired plant. (I made those numbers up by the way; but my order of magnitude is spot-on)

Not going to nitpick your made-up numbers, but the difference is that this is a bigger thing "than I want to take this risk". This is taking the risk that the area become a nuclear wasteland (from radiation, not explosion) for the next 100 years, an area that no person can enter without risking their immediate health just by being present. If you get too close to the hotspots without the right gear and monitoring, you will die quickly.

Are other things dirty? Do other things have tradeoffs and downsides? Is there even some risk that nearby property will be damaged or destroyed? Sure. I'm not trying to say that other industrial accidents are no big deal. But nuclear is the only thing that can, almost instantly, take a big chunk of land and permanently and irrevocably irradiate it for 100 years (and, that's just the most severe risk with nuclear power generation; there are others that haven't been discussed).

You can say that greenhouse gasses have the same potential non-local impact, which is fine, but quite the inverse of nuclear power, greenhouse gas emissions take decades to effect this impact and are measurable and controllable. We know it's coming and can do things to stop it.

As far as I know, the most catastrophic failure at a conventional plant would impact local air quality temporarily. The most catastrophic failure at a nuclear plant can impact everything about the surrounding area (for loose values of "surrounding"; Chernobyl created a 1000 sq mile no-go zone) for generations. Those failures can and do happen overnight.

Chernobyl happened. Fukushima happened. If a similar incident happened at the plant just north of NYC, the evacuation zone would include hundreds of thousands or millions of people.