It is absolutely pilotable, but it generally doesn’t make sense economically to do so: most of the cost of electricity production is fixed regardless of the output.
EDF says they are able to make their reactors go up or down by 80% in 30 minutes, it’s not as good as hydro or gas but it’s certainly something
Radioactive waste is obviously dangerous (though to varying degrees, most of it, by volume, is very weakly contaminated if at all), but so are all the chemical wastes from processing ores etc, and for some reason we don’t talk about keeping these secured for as long as they’re dangerous (and unlike radioactive waste, they don’t necessarily become less dangerous over time). And the volume of chemical waste is way higher.
Thinking about nuclear waste is good, but in the same process, you should also think about the environmental damage necessary to produce solar panels. A rarely depicted advantage of nuclear is the relative small amount of material needed to produce that amount of power (including the building of the power plant), and that has huge consequences for pollution upstream, and therefore, safety.
Edit: to be clear, I am not against solar panels in any way, but we should be sure to include all the relevant measurements for all technologies
That often works in my experience, and can lead to funny moments