Because the actual amount of waste that has to be stored for that long is minimal and can be shoved kilometers down into the earth’s crust with the same tech that’s used to extract oil. Nuclear waste storage is a great headline topic but there have been a lot of innovations in the past ~50 years.

As for lower tiers of waste (as in, less dangerous, more numerous, mostly consisting of stuff like tools used to work on the power plants, which is what actually goes in the yellow barrels usually depicted with grey goo), several reactor projects existed that actively used that radioactive waste for even more energy generation, usually targeted extremely hard by anti-nuclear activists because it would take away their talking points. The science exists, the opposition is usually political and driven by fear tactics. But this is why we store those lower tiers of nuclear waste on the surface, not because it’s the best place to put it but because it’s where we can retrieve it once we find a use for it.

And again, consider the alternative. Fossils also fuck up the environment and it’s not a good thing that they do it faster. The only way their effect would go away that fast is mass genocide of the ecoterrorist flavor, and exactly what future generations are we talking about in that case?