You appear to be reiterating an irrational position. I provided links to overviews of the topic; I strongly suggest at least skimming them. The quantity of unavoidable high level waste would appear to be sufficiently small that geological disposal is a cost effective solution.
The high level waste in question is not magically safe. Rather the various reprocessing and disposal methods have been extensively engineered and deliberated. At this point there is no cause to believe deep geological disposal in crystalline bedrock to be unsafe.
I said from the start that the argument you presented was fallacious, and all you did was present it, now, because you have no other argument, you're working on aggressive attacks.
Do please explain how it's fallacious? I've made the claims that one, there is a sufficiently low volume of waste produced per unit of generation that geologic disposal is affordable and scalable and that two, said geological disposal is in fact safe. Where's the fallacy?
It appears to me that you are attached to a position that you aren't capable of defending.
Also worth seeing that less has to be fundamentally safe at some point, otherwise background radiation would be a threat. If examined on its own without considering the surrounding inert volume, one decaying particle is presumably quite radioactive.
So since less->magically safer is true some point, the argument can't be made fallacious by asserting it is true. The worst the argument can be is unpersuasive (although it is persuasive - from a practical perspective there is a tiny volume of toxic waste, it isn't a reason to block progress).
Less waste to deal with makes it safer, simply because you need to control and manage less material.
We also know how to get rid of it entirely, leaving only material that will decay to safe levels within hundreds of years. It's prohibitively expensive right now, but may be feasible in the future once technology matures.
It's called "closed [nuclear] fuel cycle". Just google it. I studied it at a university.
TLDR; if you have enough fast neutrons, you can transmute anything into safe materials. Fast neutron reactors produce enough, classic PWR reactors do not. The only commercial fast reactor right now is in Russia.
If at some point humanity decides to stop making reactors altogether, it's still possible to burn the waste with particle accelerators. It'll take hundreds of years, but waste won't be going anywhere.
And finally, if commercial fusion reactors ever happen, they can also be used as neutron sources to trivially burn up all the waste.
In the US reprocessing of civilian nuclear waste was stopped not for technical reasons, but for political reasons. The primary reasoning was that: US reprocessing of civilian nuclear waste would encourage other non-nuclear weapon states to build nuclear reprocessing capabilities which would make easier access to plutonium - nuclear weapon material.
"On April 7, 1977, President Jimmy Carter announced that the United States would defer indefinitely the reprocessing of spent nuclear reactor fuel. He stated that after extensive examination of the issues, he had reached the conclusion that this action was necessary to reduce the serious threat of nuclear weapons proliferation, and that by setting this example, the U. S. would encourage other nations to follow its lead."
Commercial fusion reactors could be used burn (transmutate) long-term transuranic waste, on the other hand they will produce short-term nuclear waste, like neutron activated steels.
Yeah. My former coworker was researching ways to make steel less "activatable". Turns out that the most problematic contaminant is niobium, so he was working on possible ways to remove it completely.
The proliferation risk was real at that time, but it's now a moot point. The details of plutonium refining are well known.
Principles of plutonium separation are well known (https://en.wikipedia.org/wiki/PUREX), but preventing non-nuclear weapon states from having access to nuclear materials usable for nuclear weapons (Plutonium, Highly enriched uranium) is still cornerstone of US foreign policy. See the current events in Iran. Or the discussions with South Korea:
"The U.S. State Department did not give specific responses when asked if the U.S. was open to changing the agreement and what sort of discussions it had agreed to, but a spokesperson said:
"America has a longstanding policy to limit the spread of enrichment and reprocessing capabilities around the world and to seek the highest nonproliferation standards achievable in all 123 agreements.""
This also the reason for monitoring and inspections by International Atomic Energy Agency in all facilities handling nuclear materials (nuclear reactors, fuel manufacturing, nuclear waste storage) or capable of producing nuclear materials - in non-nuclear weapon states.
There's very little waste that lasts hundreds of years, and the reason it's "prohibitively expensive to store" is purely political. Because we safely and cheaply store it now while waiting for multi-decade trillion-dollar projects drilling deep mountain storage close to magma or something.
You do understand that don't you?