anywhere from thousands of years to millions of years

only in a strictly thermal reactor environment, if you're using a fast reactor, something like the SSR that is currently being worked on in canada, it can both burn waste, and reduce it's lifespan to a much more reasonable length.

As always, development is the problem, if we had more energy being focused on this, we would be farther along, but such is scientific development.

solar cells have no mechanically moving parts

ironically, large grid tie systems are starting to "emulate" the spinning mass behavior of turbine generators, since there's an exponential failure issue waiting to crop up if you aren't careful, as texas has already learned, a very significant part of your solar generation can just, go offline, if it decides grid conditions aren't suitable, which can lead to LARGE drops in power production and frequency, which is likely to kill even more generation.

So the solution is to make it emulate the physical mass tied to a turbine, or at least, more generously provide power in fault like conditions, to prevent this sort of exponential breakdown of the grid. You could of course, use a large spinning flywheel to regulate grid frequency, as is being used in a few places right now. I'm not sure how popular that is, outside of wind energy. It's likely to get more popular though.

weird little side tangent, but the frequency of electricity on the grid is essentially directly tied to the rotational speed of all turbines currently on the grid, meaning there is a very large inertia in the grid frequency, it's weird to think about, but makes perfect sense, and it provides for an interesting problem to solve at large scales like this.

Batteries are really fucking cool btw, the fact that you can just chemically store electricity, and then use it, is really fucking crazy. The fact that it's the most accessible technology is also insane to me. But maybe it's just the adoption being the way it is.