Is the waste really that large? I was under the impression that the waste was rather manageable.
There's a common sleight of hand where you talk about nuclear waste and proponents will reply something like, 'You could fit all of the spent nuclear fuel from the US in a football field.' -- which is technically true if the waste was stacked 30 feet high. But the real sleight of hand is the switch between Waste <-> Fuel.
Nuclear fuel is something like 2% of the total volume of waste that must be dealt with. It's the highest activity waste and the most dangerous so it's given the most credence but there are orders of magnitude more waste generated that also must be safely stored away from humanity for dozens-hundreds of years. From the initial fuel processing biproducts, to activated components in reactors, to resins and claddings, just tons and tons of dangerous radioactive material. Then beyond that, there's another few orders of magnitude of low-level waste that is less dangerous still but can't be just buried in a dump.
There are processes to turn the liquid components into glass and encase the rest in iron and concrete but just add it to the list of things we haven't really "solved" in order to form a responsible nuclear civilization.
If delaying nuclear until we “fully solved” nuclear waste means that tens of thousands of Asians die of lung diseases every year instead, maybe a half-solution is good enough.
Weapons proliferation via (theft and) reprocessing of the much greater amount of high-level nuclear waste resulting from a “nuclear future” is the real thorn in the rose.
Low level waste is the largest by volume by the way, so mostly not related to nuclear reactors.