But what's going to happen with the nuclear waste? I've heard too many times about water getting into permanent repositories and leaking containers contaminating the biosphere. Seems like a bad idea to me...
There's no fundamental problem with it, since it's produced naturally as well [1] and sites exist that would allow for very safe long term storage if need be.
It's also possible to get rid of long lived decay products entirely using certain types of reactors that can "burn" nuclear waste.
Again, political will and major investments would be required to make that happen, though some companies are already working on it.
France does so, Japan does so, even Poland sold off nuclear waste from research reactors for reprocessing - the parts of it that aren't critical medical radioisotopes, which we sold separately for use in hospitals etc.
All of French fuel waste fits in one hall. That's smaller than space taken by one fly ash repository at a coal plant.