That's why we've already seen breakthroughs in reactors that use nuclear waste for fuel.

We would have had that solved a long time ago if it weren't for a few factors.

The first is that a significant amount of radioactive waste is short-term. Like, literally inert after a couple years. The reason for that is because the vast majority of radioactive waste isn't actually inherently radioactive. Most of it has become radioactive as a result of coming into extended contact with highly radioactive sources. However my understanding is that despite being short-lived, you must dispose of it the same way you'd dispose of nuclear fuel rods. This is an issue that could be resolved by separating the short-lived stuff from the fuel rods and returning the short-lived stuff to a landfill once radioactivity drops to background radiation levels.

Factor 2: paranoia. We had a potential permanent waste site in the middle of nowhere, in an extremely geologically stable area in the US that has virtually no chance of flooding, however people thought that radioactive waste buried beneath a literal mountain would somehow still poison them. So Yucca Mountain was never fully completed. Afaik it's technically still on the table but it's been completely defunded thanks to NIMBYs, so instead nuclear waste is being stored across the US at various nuclear plants which are less geologically stable, have a higher chance for flooding, etc. This also hampers state and national efforts to clean up decommissioned plants and nuclear accidents. The waste has to go somewhere; if you have no where to safely store it, you can't clean it up.

Factor 3: if I understand correctly, we could hypothetically design nuclear plants with reactor chains that produce dead fuel rods (fuel rods that are completely spent). However, a lot of weapons-grade material would be produced during the intermediate stages. For sooome reason everyone freaks out when they hear you're making weapons-grade radioactive material, even if you promise you're just using it to generate power. I can't imagine why /s

The problems with nuclear storage are actually pretty easily solved, it's just that no one wants to because they'd rather pretend nuclear doesn't exist to begin with. I swear, we could have a one-time pill that makes you fully immune to every radiation-induced disease and people would still freak out about nuclear. Hell, there was an article I saw a month or two about how a bunch of researches discovered that turning used graphite control rods into diamonds resulted in low-power batteries that could be used for things that require a small amount of power over long durations (like SSDs or RAM). Iirc something about the diamond's structure meant it contained its own radiation as well, meaning it didn't need any radiation shielding either despite generating energy via radioactivity.

It's still better than the totally uncontained pollution and carbon dioxide of fossil fuels.

It's better than what we are doing to limit the emissions from petroleum.

And the non insurable nature of nuclear power besides its distant break even point is the reason only governments have ever build nuclear plants, or had to give huge guarantees. There are financial problems with nuclear, too.