The data is sparse because the rate is very low. If the world used twice as much nuclear power as it does now, we don't have enough statistical data to predict with high accuracy if something as bad as Chernobyl would happen two more times or zero more times but the existing data allows us to be pretty confident it wouldn't be 100 more times. Meanwhile coal kills more people than 100 Chernobyls every year in just the US.

There is also reason to suspect Chernobyl was an outlier because the USSR was such an authoritarian nightmare. They not only screwed up the design of the reactor (positive void coefficient, no containment building) but then also its operation and the response. The majority of the confirmed deaths were plant workers and emergency responders who got radiation exposure after being sent in without training or relevant equipment. It took the USSR more than three days to admit that it had even happened so that people living next to the plant would know to leave the immediate area. Screwing it up that bad required more than an honest mistake.

> Especially long-term storage is tricky, and if you need to consider time horizons of millenia, even small risks add up.

The "thousands of years" thing is essentially fake. Radiological half-life is the inverse of intensity. Things with a half-life of five minutes are super radioactive. Things with a half-life of thousands of years are barely above background.

For example, there is an isotope of uranium that has a half-life of four billion years. It's also a pain because its decay chain contains radon gas. ZOMG what are we going to do with it for that long? Well, that's the one that represents 99.3% of natural uranium straight out of the ground, which is why homes in areas with natural granite need radon reduction systems, so it turns out the answer to what we do with it is we can put it in a reactor and use it to generate electricity and that will turn it into something with a shorter half life that goes away sooner. And the major ones that are "thousands of years" can also be used to generate electricity if we would actually separate them and use them for that to get rid of them instead of wringing our hands about what where we're supposed to keep them.

> In fairness, you then also have to consider "regular" industrial accidents at nuclear plants, which are probably still much lower (due to the presumably much higher energy output per employee hour than other forms).

It's also lower because nuclear plants are pretty obsessive about safety vs. random solar installation company whose job application test is to see if you can make it onto a third story roof with a two story ladder.