Wherever it is put the high level waste (not much in quantity but...) is deadly and a silent killer for over a hundred thousand years. This is geologically significant time period, and we can make bets, but have no guarantee of any place on Earth being stable on those time scales.

So it must be monitored.

For a hundred thousand years

That would be us making future generations pay for the cost of our current consumptions. I do not think they will think kindly of us.

- Extinction - We don't need to care about it, because there are no descendants.

- Advancement - We will be able to handle the problem better as our technology improves.

- Stagnation/regression - We don't need to care about it. Our descendants will have to worry about dysentery, crop failures and regional warfare. Some magic rocks that kill people will end up as curios in warded laden boxes after first adventurous monk opens sarcophagus and succumbs to curse.

The geological pixel - smallest possible measurable period - is 50,000 years. Nuclear waste is 2 pixels.

Everest is a 50 million years old. The chalk that makes up white cliffs of dover is 130 million years old. There are layers of bedrock over a billion years old.

So yes, we are making a bet in the sence that when I go putside I make a bet that an asteroid won't fall on my head.

Leaving piles of toxic waste - either nuclear or some other nefarious thing you are implying - is due to greed.

Can we deal with our greed?

What's left is just fission products. Encase them in glass and bury them, and they'll be back to the radioactivity of the original ore in 300 years. Most of the radioactivity will be gone in the first few decades, since the decline is exponential.

Russia has a couple fast reactors in operation right now, and various startups are attempting new designs.

It does not really matter how big the caverns are where you store the waste so any additional nuclear material stored is basically free.