The world has converged on the most economical solution to spent fuel: dry cask storage. This is not an ultimate solution, but it forecloses no ultimate solution, and by delaying any such expensive step it minimizes the net present value of the cost of dealing with the waste. In the meantime, the spent fuel gradually cools off, rendering any future ultimate solution easier.
Reprocessing can be seen as a fossilized remnant of an earlier failed vision of where nuclear power was going to go. The vision was that nuclear power plants would be cheap, lots of them would be built, and then uranium would start to run out. Fuel would start getting expensive, so we'd have to move to breeder reactors. Fast breeders burn plutonium, so you want to start them with Pu separated from the earlier thermal reactors (and then continue to fuel them with Pu they themselves produce.)
But this vision never came to pass. Nuclear power plants turned out to be expensive and uranium remained cheap (and enrichment got cheap). Reprocessing ended up unneeded and unwanted. It really did serve as a cover for proliferation, too: Japan now has enough separated reactor grade Pu for about 1000 bombs. It's not as good as weapons grade but it can still serve for weapons if boosting is used to ameliorate premature initiation of the chain reaction.
There's an inversion of cause and effect here. Nuclear didn't fail because we didn't reprocess, we didn't reprocess because nuclear failed. To invert the actual causation is an example of cargo cult thinking.