Yes but you have way less waste to dispose of. In America, the Uranium and Plutonium that makes up the vast majority of spent nuclear fuel is not separated out

Yes but you have way less waste to dispose of. In America, the Uranium and Plutonium that makes up the vast majority of spent nuclear fuel is not separated out from the fission products, we just get rid of it all. IIRC reprocessing is actually slightly more expensive than just mining fresh Uranium as now you need to re-enrich the fuel anyways and Uranium is plentiful enough at least for now. By separating out the spent fuel you isolate the most radioactive components and now you can avoid having to store the majority of the fuel for extremely long periods of time. Reprocessing does not eliminate all nuclear waste, it just minimizes it to only storing the highly radioactive portions instead of the inert components. It also is a prerequisite for any of the proposals that I know about for actually eliminating the nuclear waste instead of just burying it. The long lived radioactive waste could be used as a blanket around a fusion reactor that is used as a neutron source to fission the waste and generate more energy from it.