Re: So?
"carbon free nuclear producing irradiated waste that generations will have to worry about,"
About as much to fill an olympic sized swimming pool for fuel to last the operational life of a civil 1400MW plant.
Which if left onsite, is cold enough to handle safely in less than 300 years (not 200,000) and at that point mostly consists of U238 and high grade plutonium which is usable fuel for a new plant.
On the other hand the coal plant is spewing carcinogenic shit into the air and almost all the increase in oceanic mercury in the last 200 years is attributable to burning coal. That's quite apart from the radioactives that go out the chimney when burning coal (embedded in the fuel) which worldwide add up to the equivalent of several chernobyls every year - except that because you can't see it, you don't care about it.
Of course, if you smoke, then it doesn't matter anyway - https://www.youtube.com/watch?v=TRL7o2kPqw0
radioactivity isn't particularly carcinogenic, else they wouldn't be using radiation as a cancer treatment. It's good at killing cells and not so hot at causing them to mutate. Chemicals are far better at that game. Problems with radiation exposure occur when the death rate of cells is higher than they can be replaced and that takes a LOT of exposure.
Most radioactives-derived cancers are caused by mutatgenic effects of the breakdown elements, not the radioactivity itself. In the case of smokers, that's lead, bismuth and mercury compounds sitting in your lungs after the Polonium has been fizzing for a while - all known carcinogens.
So, contrary to what you "know", the fuel which is safer for future generations is nuclear, even with todays badly flawed designs - which although "badly flawed"(*) are still several tens of thousands of times safer than coal burning plants in terms of deaths/injuries per TWh produced.
(*) The flaw is taking a steam plant designed for 6MW in a nuclear sub and scaling it up to 600-1400MW. Boiling water is a pretty good solvent, hard to contain and becomes explosive (splits into H2+O2) if heated to maximum nuclear reaction temperatures (~1200C - past that the reaction is self-limiting due to doppler effects), so having it in direct contact with nuclear fuel is a bad idea, as is relying on circulation systems to keep it cool instead of using a coolant that can safely handle those temperatures in the first place.