You still need some level of containment along with environmental studies and the additional complexity of excavating a large underground cavern. Even then, someone will be concerned (possibly rightfully so) about groundwater contamination. Fracking is a prime example of how connected that all can be.
https://en.wikipedia.org/wiki/Deep_borehole_disposal#:~:text....
https://www.latimes.com/nation/la-na-new-mexico-nuclear-dump...
A leak or accident in one of these deep-buried reactors could contaminate vast underground water reserves, rendering them unusable for generations. The environmental and human cost would be catastrophic and irreversible.
This should never be attempted.
https://en.wikipedia.org/wiki/Deep_borehole_disposal#:~:text....
These are all issues for fossil fuel extraction as well, and I have bad news for you about how this problem is currently handled.
Containment and disposal is largely a red herring. It's actually more or less a solved problem, from a safety perspective, because it turns out that the laws of exponential decay mean that you can just store it with proper shielding and it's safe for storage pretty much anywhere. I'm oversimplfying, but only a little bit - the public's perception of "nuclear waste" is extremely untethered to the actual reality.
The whole fiasco with Yucca Mountain was driven not by science, but by a desire to appease objectors by adhering to an arbitrary and unscientific perception of safety, not an actual assessment of the risks.
> while people picket nuclear facilities and wind turbines
Where are you seeing this? Nuclear energy has lost a lot of energy for active support, but active protest ("picket") of nuclear facilities is exceedingly rare these days. Wind turbines are a different matter: they're sustainable, but they're opposed by monied individuals/groups who don't want their beachfront views "ruined".
https://www.latimes.com/nation/la-na-new-mexico-nuclear-dump...
You are right though that you will never win the safety argument. Nuclear has become entrenched in our culture as a world ending bugbear. Meanwhile the actual possibility of world ending climate change is just scooting along while people picket nuclear facilities and wind turbines.