Hey first of all thanks for the constructive replies, much appreciated!
"Attempts to understand this risk by looking at historical data are flawed" is a good summary of my main point, you got it. Basically I think we can't ignore the possibility of large incidents just because they haven't happened yet.
We can extrapolate from known small incidents, some of which are listed on wikipedia:
https://en.wikipedia.org/wiki/List_of_civilian_radiation_acc...
Some standouts:
https://en.wikipedia.org/wiki/Goi%C3%A2nia_accident
https://en.wikipedia.org/wiki/1996_San_Juan_de_Dios_radiothe...
Other incidents mentioned without separate stories include radioactive waste finding its way into road pavement, apartment building materials (hundreds of contaminated flats, nobody found out for years).
Incidents such as these have killed many people over several decades in many countries, and that's just through sheer negligence. What if someone adds malice to the mix?
That's actually my main concern about nuclear power, not the safety of the reactors.
But since you mentioned building them in a desert in order to be safe I feel the need to mention my perspective there too. First of all, Chernobyl had 4 reactors and only one exploded, thanks to heroic effort. (Meaning it could at the very least have been 4x worse than it was).
The event was actually discovered in the west by sensors in Sweden, which is very far away. Fallout from Chernobyl made certain grazing animals surpass legal radiation levels for over 30 years (and counting) in areas as remote as Lapland and Bavaria.
To put the distances in perspective if you are American, it means that a similar event as Chernobyl taking place in Florida would make pigs from Texas and Caribou from Ontario be unsuitable for human consumption, for many decades.
So distance does not really help. In order to be safe by putting power plants in a desert, the USA would basically need to put it's reactors in the Sahara.
The safest place for a reactor would be inside a very stable and peaceful country with a very high level of mental health in the entire population. Maybe Switzerland?
I'm not saying we shouldn't even consider it under any circumstance, but if there's any other option (which I believe) then that option is probably preferable.