The reason I used to oppose nuclear energy is that its proponents would say nuclear waste isn't a problem, but they would never explain why it isn't a problem. I knew the half-life of uranium was 4 billion years; I didn't see how you could possibly make that safe, and nobody on the pro-nuclear side seemed to have an explanation, so I assumed that no explanation existed.

(Turns out the answer is that you can store nuclear waste deep underground at geologically stable locations where tectonics won't cause it to eventually resurface.)

(Also radioactive waste isn't uranium and the half-life is considerably shorter than 4 billion years, although it's still quite long.)

it’s also true that you get better at using (and reusing) what we would consider waste today over time.

The more energy we are able to use, the more inert the waste material becomes, leading to much lower storage timeframes (though still multiple human lifetimes even in the best case).