If we are talking about LFTR/MSR power, the waste is minimal and disappears quickly (~100’s not 100,000+ years), but let’s address the waste from standard reactors (typical US light-water). The graphic shows how fresh fuel becomes “spent” fuel and how it changes while in the reactor. At the end of the cycle, it is removed and put in a pool of water in the plant, then later transferred to more long-term storage (generally casks).
As you can see from the picture, most of the material left behind is fuel.
Put simply, “spent” fuel isn’t spent. It is roughly like burning the bark off of wood in a fire then removing the wood. A hotter fire can burn the wood and not just the bark.
There are newer reactor technologies that could consume currently available “spent” fuel, as well as Canada’s CANDU reactors.
The component that is the long-lived part of the “waste” is plutonium, which comes from U-238 absorbing a neutron (and decaying twice to plutonium). This plutonium is FUEL. If it were to be consumed, the long-lived nature of this waste would basically disappear.
There is NO long term waste issue with so-called “spent” fuel.