Handling waste isn't that difficult of a problem. There are better reactor designs which use a lot of that waste as fuel, and what's left just needs to be sealed up real good and left to sit behind some good fences.
Basically all of the real-world problems with handling nuclear waste are because anti-nuclear advocates prevent any action from being taken to handle waste, but meanwhile there are operating reactors producing waste and that hasn't stopped. So nuclear plant operators are forced into ad-hoc solutions for waste disposal because nobody will let them do it right.
You're simply hand waiving away the problems. Even reprocessing creates waste that must be dealt with. Commercial fast/breeder reactors are always ten years away, and it has yet to be proven that they could even be economically viable.
Basically all of the real-world problems with handling nuclear waste are because anti-nuclear advocates prevent any action from being taken to handle waste, but meanwhile there are operating reactors producing waste and that hasn't stopped. So nuclear plant operators are forced into ad-hoc solutions for waste disposal because nobody will let them do it right.