Please remember that burning coal also leaves behind dangerous and mildly radioactive waste, that's usually not protected in any way or form - it just sits there, washed away by rain and blown away by rain. Where I'm from(Silesia region of Poland) the ash hills are permanent feature of the landscape, and a short trip with a Geiger counter shows easily that they have higher radiation level than background. It's not very dangerous of course, but it's there.
On the other hand, actual nuclear waste is protected fantastically well, and it's not that difficult to store. We always had plans for ultra-long-term storage too, no? Deep underground in salt deposits so it would be protected against earthquakes and underground rivers.