Radioactive waste can be contained and when reprocessed as part of waste disposal
Therein lies the rub. Firstly, while you're absolutely correct when things are working properly, nuclear is very hard to clean up after things go wrong. While the immediate effect might still be reasonably small in global terms, a much larger area (and therefore politically more problemtic) is affected in a nuclear disaster than in an equivalent coal-power disaster.
An oil spill might be more comparable actually, but even there, hard radiation is much harder to clean up, and a much more dangerous environment (to humans, at least) than oil. Oil spills also likely to be further away from human population centers (easier to transport efficiently) which, while not a sound environmental argument, is pretty sound politically.
Secondly, there's historically been some conflict of priorities between "use nuclear fuel efficiently" and "don't allow anything that could be turned into a weapon".
I'm not anti-nuclear as such, but I do think that it's politically problematic and that "environmentally safe" fission power at large scale is a lot more expensive than what we're willing to spend on energy today.