Why don't we launch the nuclear waste into deep space? Seems like that would avoid the burial problem described here, and since space is mostly, well, empty space, wouldn't inflict much harm to other bodies.
I googled a little to find a reliable set of launch success statistics but found nothing I was willing to include herein (it's Sunday morning, I got up late and am lazy right now), but overall success rates are in the high 80% to mid 90%. Failing to launch a satellite is one thing, having radioactive material spread atmospherically by a launch failure is quite another.
Then there's the cost. Yeah, that would be high. Especially with adding containers to protect against the risk described above.
If we had a more reliable means of getting the waste into space, I'd be all for this.