The challenge is a lot smaller than it is generally made out to be. Nuclear waste has a weird decay curve due to the absolute mess of isotopes it contains. That means it is insanely radioactive at first, but also decays very quickly. After a while, only the long-lived isotopes are left, but they are also not very radioactive.
We tend to conflate the two, and assume that the waste is both highly radioactive AND long-lived, but this is not the case. It is highly radioactive for a reasonable amount of time, and then low-level radioactive for a really long time.
The challenge is only how to handle it while it is incredibly radioactive, but the timescales involved are not at all impossible to deal with. Once it has cooled down, just leaving it buried is perfectly fine. There's very little long-term risk.
(Let's say, as an oversimplification, that the time of high danger is maybe two hundred years - a long time to be sure, but not unprecedented in terms of large-scale engineering projects. Around that time, the radioactivity starts dropping very sharply.)
The challenge even at low radioactivity is materials for containment. If containers are damaged by the waste, as they likely will be over long durations, than refreshing the containers is insanely complex and fraught with hazards.
We tend to conflate the two, and assume that the waste is both highly radioactive AND long-lived, but this is not the case. It is highly radioactive for a reasonable amount of time, and then low-level radioactive for a really long time.
The challenge is only how to handle it while it is incredibly radioactive, but the timescales involved are not at all impossible to deal with. Once it has cooled down, just leaving it buried is perfectly fine. There's very little long-term risk.
(Let's say, as an oversimplification, that the time of high danger is maybe two hundred years - a long time to be sure, but not unprecedented in terms of large-scale engineering projects. Around that time, the radioactivity starts dropping very sharply.)