I LOATHE this whole concept, because it's just so stupid in SO many different ways. I'll just pick 3 of them, based on how we manage other hazardous waste, and basic human history.

1 - we've got chemical waste sites that will stay dangerous FOREVER. not for 10.000 years, but until the end of time, which are far more dangerous than nuclear waste. Mercury compounds, pesticides, stuff like per- and trichloroethane, and numerous volatile compounds that's we've disposed of. We put them in managed sites, and the way we make sure they stay safe is to monitor them forever. There are orders of magnitude more chemical waste, that is orders of magnitude more dangerous, and nobody really cares about it because there is a working solution. But for nuclear waste, suddenly we require some kind of magical super-site where we can just drop it and walk away. WHY?

1b. - Let me also point out that much of what we previously considered dangerous waste is now a valuable resource. Cokes are now great ballast and filler materials, fly-ash is used in concrete and the places where we buried it were suddently worth millions, polluted soil makes for great aggregate in concrete, etc. etc. etc. We ALREADY know that spent nuclear fuel is still very useful as new fuel, so preparing to put it away forever is just stupid. We will absolutely be digging it back up in a before this facility has even spent 5% of its designed lifetime.

2 - This site is useful in only a single use case. Sometimes between now and when it's "safe", humanity has an enormous catastrophe before we figure out a way to make it economically and politically viable to re-use the nuclear waste as more fuel, which causes us to forget everything we know this place, science and written language. This would likely means billions would have died. Then, after we recolonize this locations, we supremely care about a few dozen more deaths of some hypothetical future humans, who are far more likely to die from exposure, malnutrition, disease, hungry wolves, etc etc. Unless these specific events happen in this order, it's just a useless art project discussed by people who are wasting huge amount of time, effort and money. If you want to save future humans, there are so, SO many more useful ways to spend your money.

3 - Humans aren't fucking morons (well, individuals are, but as a species there's a reason there's so many of us) We've always understand where it's dangerous to live, what's dangerous to eat, what things are more likely to kill you than other things. Post-apocalyptic, non-technological humans will figure out very quickly that they shouldn't scoot up to the glowy warm metal. Non-post-apocalyptic humans will know what this place is, because they're not fucking idiots.

The solution is ray cats, I tell ya. If the kitty's glowin' you better be goin'.

The 99% Invisible podcast did an interesting episode on this topic, too.