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Contrary to popular belief, nuclear waste isn't this sizzling highly-radioactive goo that kills everything that it gets close to. It's mostly stuff from the reactors and not even the spent fuel itself. By the time it's moved off-site from the plant, it's only minimally radioactive and is perfectly safe so long as it stays inside the containers. Obviously you don't want that shit leaking into the groundwater or breaking apart and turning to dust that someone could inhale, and the "minimal" radiation will last for thousands of years, but it's not that bad.
The reason why they wanted to put it in Yucca Mountain has less to do with it being desolate and more to do with it NOT being geologically active or subject to erosion. They're not thinking "where can we put this stuff where it won't be disturbed for a century" they're thinking "where can we put this stuff where it won't be disturbed until at least the year 50000, even if nobody is around to maintain it.
Chernobyl isn't just some empty crater where nobody goes. The still-contaminated materials need to be maintained frequently so things don't get a whole lot worse (like, as mentioned, leaking into groundwater or drifting into the wind) . They just recently finished a brand-new structure to enclose the busted reactor, something which will hopefully last 50 years or so. But then they'll have to replace it again. And again. And again. And so on for centuries until it becomes safe enough. But the cost of fucking that up is irradiating millions of people.
What you're proposing is to create more of that kind of work. Rather than bury it in a safe place, you want it... what, exactly? Just sitting out on the streets of Pripyat in the wind and the rain??
