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".