Ok, storing carbon in the air and oceans is much more practical as it basically comes for free. Well, not counting in the cost of climate change of course.
Burying atomic waste on the other hand requires laughable amounts of space if you want to compare atomic waste vs carbon for let's say 100 years of global energy production. We already have to deal with the "catastrophic failure" of carbon storage as a "future generation" as you already mentioned.
I know a lot of people like to imagine that getting rid of atomic waste is basically some people with shovels digging holes for some hazardous yellow barrels, hoping in a thousand years no one will find them. Well, no. Atomic waste is much more manageable. And to be honest: If we had a way to say efficiently compact/solidify/whatever carbon then we would do the same with that stuff today already, just with the difference that we would leave much much much more waste behind for future generations.