That was the Mayak reprocessing plant, not a storage site.
Also, the radioactive substance released there was a liquid, spent nuclear fuel is a bundle of metal rods.
Yuccan is not a good place to bury Waste anyway. Nowhere is. Except probably the earth's core.
Neither are cheap. But both will get rid of ti forever
Commercial rockets in general have a very high failure rate. The fact that no Saturn V blew up is mostly just luck.
Spent nuclear fuel is also ridiculously dense. One ton of uranium takes up as much space as a typical computer case.
You would have to launch hundreds of Saturn V's to get rid of all the waste, something that's extremely risky and nation-bankruptingly expensive.
Putting the waste hundreds of meters below the surface and above the water table in geologically stable bedrock will keep it isolated until it has decayed to a safe level.
Any natural phenomenon that can erode hundreds of meters of rock or raise the water table by hundreds of meters in less than 100.000 years is a much bigger threat to humanity than nuclear waste. I'm talking about stuff like Ice Ages and extinction level comet impacts.
The former won't happen at Yucca mountain unless the whole planet turns into a snowball.