Just look at the statistics. E. g. https://en.wikipedia.org/wiki/Lists_of_nuclear_disasters_and...
To say that they're _potentially_ safe by waving at the US Navy is a fallacy for several reasons.
1. It's p-hacking. E. g. with the same technology the Soviets destroyed five of their reactors.
2. The world of civilian operators is completely incomparable.
3. Civilian power plants use different technologies.
> Waste is mostly a solved problem.
Not as far as I know. In Germany, for example, the search for a final disposal site is still completely open-ended, and the first final disposal site will not open until 2074 at the earliest, while, at the same time, the already collapsed storage facilities consume an enormous amount of money. I personally think it is absurd to assume that an underground nuclear waste storage facility can be operated safely over geological time scales. Needless to say there isn't even a single one worldwide for highly radioactive waste.
And to compare them with coal plants is classical whataboutism. "They can't be bad, because I found something other that's bad as well."
You're right about the minable uranium. That has changed over the last years, so the current estimate is 2080 in a high demand scenario.
But your criticism about the externalized costs falls short as well. Regarding the externalized costs, that is really hard to quantify and I don't know of reliable estimations. How do you want to come up with a number if you don't even know if humans still exist on the planet at that time?
What is clear is that for nuclear energy the majority of the costs is externalized. The bulk of the costs stem from the decommissioning of power plants, final disposal, and accident-related expenses. All three are typically passed on entirely to taxpayers.
The former German vice chancellor even said, he would agree [to build a new nuclear power plant] if <political opponent> found a private operator willing to build a nuclear power plant entirely without government guarantees, subsidies, or liability coverage.