This "problem" is why we need nuclear. You can't store power generated by solar and wind, so when the sun goes down or the wind dies down, the power goes out unless you rely on some other source. Nuclear can work every hour of the day. It's the only power generation method which can supply power at every hour of the day and can be deployed almost everywhere (hydroelectric is neat but you're screwed if you don't have a good river). All these other "problems" have been written about extensively by specialists, just not by journalists.
As for the rest of your problems with nuclear specifically, I don't think you're comparing the negatives of nuclear with the negatives of literally any other power source.
The real reason we won't go nuclear is that Democrats and progressives don't like it because it's scary and makes them quake at night. We could use nuclear as one tool in fighting climate change, but we aren't willing to do that. We're dying by our own hands.