The waste is the biggest advantage of nuclear. Consider that when you burn hydrocarbons, you produce waste, too. And much of that waste is simply dumped into the air where we all breathe it.

You might say, well, hydrocarbon waste is much less dangerous. But that's negated by the fact that you need about 1,000,000x as much coal to replace the energy provided by nuclear. And in fact, the total amount of radioactive contaminants in that quantity of coal is roughly equal to the amount of nuclear fuel you would have required in the first place had you just used nuclear alone!