It is mostly because of military influences (proliferation risk) and environmental activism that these solutions have never been fully developed and deployed.
It's much more risky than just leaving the waste in a pond cooling for 20 years while hoping that you will be retired before someone actually have to get rid of it.
I'd say that activism has left us with the most undesirable outcome: we still have ancient reactor designs producing unmanageable waste, and every solution to actually reduce that waste has become politically unfeasible. All that we've done is create massive amounts of technical debt that will burden generations to come.
Once you take all these issues into consideration you just need to extrapolate and see how nuclear accidents will happen once in a while.
Having to store some of it isolated for 10000 years is a concern, yes, especially if you look at the average lifespan of human civilizations. But we already have ways to reuse the waste (fast breeder reactors), and we could likely figure out many more - but reluctance to fund nuclear research and applications, driven partly by the fear of "the waste", is not helping here.
On that scale, putting something away for 10K years seems relatively trivial and safe compared to CO2.
Make charcoal from wood?