The plan in the US was to enrich waste in breeder reactors, mix in some fresh fuel, and re-use it. It was the nuclear fuel cycle. Lots of resources on the technology.

There were two problems. The use of breeder reactors had some proliferation concerns: they can be used to make warheads. Not a big deal in the US, as the US can already make warheads, but harder if you want to export nuclear waste reprocessing to other countries.

Transporting the waste was deemed risky. More so after 9/11, as fresh waste is so radioactively hot, it needs to be kept in water, or it will overheat. If you crash a plane into a transport vehicle, or a re-processing plant, it will create quite a mess.

So there is no way the nuclear waste will stay in the ground for 10,000 years. I suspect it will be less than a hundred years before someone digs it up, and reprocesses it.

Burying nuclear waste is itself waste.