And what have they said about the millenia-spanning effects of the waste?

About reactor malfunctions and fallout?

Yes, I know the chances are slim and you know as well as I do they're not 0.

Nothing man-made is perfect, not even nuclear. But even with the two big accidents, nuclear is the safest form of energy generation we have. By far.

The actual safety is almost entirely unrelated to the fears people have. There is even a term for this: radiophobia.

https://en.wikipedia.org/wiki/Radiophobia

Radiophobia is an irrational or excessive fear of ionizing radiation, leading to overestimating the health risks of radiation compared to other risks. It can impede rational decision-making and contribute to counter-productive behavior and policies.