So long as it's stored in stable geologic formations, or controlled by stable human institutions. Where "stable" is a period of time longer than human history in many cases.
>does not migrate when handled properly in containment pools
Which are dependent on active management and security indefinitely. This is challenging as the service life of the plant where the pool is located and revenue is generated is less than indefinately.
> can be reprocessed if required.
Which is also a proliferation risk.
Obviously you haven't looked into the cost of enriching nuclear waste. It is prohibitively high for all but dedicated nation-state actors, who if have the technology to enrich radioactive materials to weapon-grade material aren't going to use nuclear waste.
Worst case for proliferation is being used in a dirty bomb, which just kind of spreads the waste across a limited area. Even then you're looking at alpha-emitting particles that won't cause any radioactive damage unless you ingest it. Take a shower and you'll be fine.
We've had not one but several nuclear disasters in the past several decades and in each case the sky hasn't come crashing down.
The risks from a nuclear plant disaster are localized and controllable.
The risks from runaway climate change are global and uncontrollable.
The planet is going to be fine. Whether human society survives is going to be a whole different matter entirely.
Unless of course you're one of the people who lived in the nuclear exclusion zones created by Chernobyl and Fukushima, in which case, yes, everything you own and possess, very potentially including your long-term health, were destroyed in a matter of hours. Those residents can never go back for more than a quick temporary visit, and they can not take back their belongings because they've been irradiated. They will always be asking themselves if they got enough of a dose of radiation to cause early disease.
Call that localized and controllable all you want, and if you propose building these plants in areas with no nearby inhabitants for many sq miles, maybe it works OK. The current system, where we say "Don't worry, it's all perfectly safe, we double-pinkie-promise that we won't make the mistakes those guys in Ukraine or Japan made, and if you disagree you're an idiot who hates science" is just not going to fly.
This is not general alarmism about being unable to mitigate every risk in life. This is a comparative analysis of the potential risk profiles of fossil fuels and nuclear, and fossil fuels being much better because the cost of a catastrophic non-nuclear failure is much smaller than the cost of a catastrophic nuclear failure.
When you account for the full lifecycle of fossil fuels, from the extraction, refining, transportation, and ultimate consumption and measure that impact in both short-term impact (coal-mining deaths) vs. long-term impact (climate change, pollution, cancer) you'd find that nuclear is the best option.
I'd risk a %0.00001 chance of dying by cancer sooner living next to a nuclear plant vs. a 1.0% chance of dying in a road collision with a fuel tanker or a 0.05% chance of dying sooner with emphysema by living close to a coal-fired plant. (I made those numbers up by the way; but my order of magnitude is spot-on)
As a person who worked in this industry, understands the economics of it, and has compared the costs of coal/wind/gas/nuclear, I can confidently say that nuclear can be safe and affordable as an energy source if we are committed to safe and conscientious use of it.
(BTW, for a month, I slept next to a nuclear reactor that was approximately 500 feet away from my bunk. My total radiation dose for that trip was less than I'd get in the same time hanging out at Grand Central Terminal (a location that would it to be certified as a functioning nuclear reactor would be out of specification as emitting too great a dose of radiation to those who work there)
http://www.pbs.org/wgbh/pages/frontline/shows/reaction/inter...
Yes the planet's going to be fine, in the sense that a spherical mass will continue to orbit the sun.
But if every species but the cockroach is wiped out from runaway biological ecosystem collapse, is that really "being fine"?