Something can be highly radioactive for a short time, moderately radioactive for a long time, or slightly radioactive for a very long time.
If something is “radioactive for millenia” then it’s probably so mild that you could store in your underpants without I’ll effects.
Have a little snack consisting of 1 gram of americium and 7 grams of neptunium 237, or store an equivalently active gamma emitter in your underpants.
Also, it's a exponential decay curve, so something that's slightly radioactive a very long time from now is probably still fairly dangerous right now.
"Cost estimate for MOX facility at Savannah River Site swells to $47.5 billion"
https://www.augustachronicle.com/story/news/2015/04/22/cost-...
"US MOX facility contract terminated"
https://world-nuclear-news.org/Articles/US-MOX-facility-cont...
https://en.wikipedia.org/wiki/Savannah_River_Site#MOX_Fuel_F...
The waste that remains after reprocessing in a fast cycle are fission products that will decay so much in 1000 years that the waste is less radioactive than the original uranium ore.
Cs137 and Sr90 lasting 'mere' centuries isn't helping your case any. Especially when existing MOX programs spill more than Fukushima and TMI combined as standard operating procedure.
With larger timescales, my understanding is that the mountain itself might disrupt the cube + drums, opening Pandora’s box.
Perhaps an actual geologist can weigh in and correct me.
100,000 not so much. All kinds of things can go wrong. It is expected for instance that as Yucca Mountain cools down water will infiltrate. Uranium is water soluble so some will migrate in the direction of Death Valley. Uranium is toxic the same way lead and mercury are and that is more dangerous than the radiotoxicity of uranium.
A "once through" repository will contain valuable plutonium and uranium. People might want to drill into it 10,000 years from now because they want to use it as a power source or to make nuclear explosives. For that matter we could change our minds and decide we want to recycle the waste in Yucca Mountain after all so we have to be able to retrieve the waste in the first 100 years.
A waste repository used for fission products can use highly secure but difficult to reverse approaches such as encapsulation in a salt dome or burial in areas at sea where sedimentation is taking place where waste would get deeper and deeper year after year and be blocked from migration by the tendency of ions to get trapped in clay.
Existing renewable tech + storage will do the job just fine in most of the world, and at lower cost than nuclear.
So it space and were actively trying to send people up there to live and colonize.
https://en.m.wikipedia.org/wiki/Banqiao_Dam
Coal is far, far worse than this.
Did someone think the plutonium was going to disappear?
This is why ALL nuclear power is a disaster. Even after this material is used to boil water for a few years, it's still highly radioactive for millennia.