Coal in particular results in incredible toxic waste. Even if it was inert (which it very much is not) you get enormous heaps of rock you dug the coal out of and those have to be stored forever. Typically people just leave it in a big pile as somebody else's problem until one day the wind blows and it collapses and kills a bunch of people. Oops.
But even for natural gas in the best case your waste is excess carbon dioxide, which renders your planet inhospitable so that's not great either.
Here’s a guy kissing nuclear waste. It’s a bit tongue in cheek on the surface, but he’s PhD and there is quality information in the video.
Try to list the countries with a permanent nuclear storage site. Pretty short list.
The technical front, however, really is fine.
All the high-level nuclear waste on Earth would fit in a 21m cube. The lower level stuff is substantially greater in volume, but overall this is one of the (IMO few) cases where nuclear proponent's arguments about energy density do actually matter.
And that means it's fine for the list of countries with a permanent nuclear storage site to be pretty short.
https://en.wikipedia.org/wiki/Yucca_Mountain_nuclear_waste_r...
https://en.wikipedia.org/wiki/Onkalo_spent_nuclear_fuel_repo...
What a comparison... The worry with nuclear waste is of course that the shielding doesn't last long enough and waste then contaminates surroundings with much much higher radiation than in coal ash
