> Failure modes
Making 1000 square miles of land uninhabitable for decades doesn't kill people, though. (It doesn't even harm the land, in the long term; it's sort of a good thing, decades later, like letting farmland lay fallow.) With modern technology, as was employed at Fukushima, everyone was safely evacuated from the region and literally nobody died from radiation poisoning.
Coal plants pollute globally very slowly. Coal plants pollute locally very quickly, and are capable under the right conditions of disasters just as bad as radiation fallout from our bad old nuclear plants. Have you heard of the https://en.wikipedia.org/wiki/Great_Smog_of_London ? Killed 4000, poisoned 100,000 more. And that was just a regular day of the life of London's coal plants, combined with some bad weather. So the coal plants were just fine, and kept on going after that. Meaning that there were other days like that, both before and after (if not quite as bad.) It's like a nuclear power plant that can "melt down" at random, without harming itself, enabling it to keep "melting down" over and over!
> Coal vs nuclear is a straw man argument.
No; it's the real decision that developing countries (and rural areas of developed countries) are making every day: keep building coal plants, or replace some of them with nuclear plants?
Nuclear is a viable consideration for these places in that it is a drop-in replacement for a coal plant that doesn't require any additional infrastructure to connect the plant to the mine+refinery: before, you were shipping rocks on a road to a plant; now you're still shipping rocks (well, pressed rock powder) on a road to a plant. You can even reuse the mining equipment you had from the coal mining! And, often, you have a head-start on the work, as (quoting Wikipedia): "Lignite deposits (soft brown coal) can contain significant uranium mineralization." Your coal mines have probably already excavated some, and now just have it laying around feeding no domestic industry!
Meanwhile, oil or LNG requires building pipelines, different extraction equipment, etc. And affordable solar or wind—which inevitably means domestically produced solar or wind equipment—requires a whole electronics and materials industry, and is only workable in some countries to begin with.
(The real third contender for these countries is hydro power. Doesn't require shipping anything to the plant! Much bigger civil engineering project, though, and each one is a one-off design that has its own devastating failure modes, which makes them possibly more scary to government buyers than nuclear power, where at least you can buy a cookie-cutter copy of a successful plant.)
> depending on the country I'm not sure if [state-owned plants are] better or worse
Usually far better, in that ultimately most externalities come back to bite a government (in the form of e.g. decreased GDP, and thus less taxable income), so they have far more of an incentive to clean up their act than an individual corporation does.