On the specific topic of reprocessing though. Reprocessing achieves 2 things: 1. it can extract usable fissile fuel from spent fuel, and 2. it can reduce the amount of long lived radioactive waste, by a factor of 30. Point 1 can be further split in 1.a. usable fuel for the current generation reactors and 1.b. usable fuel for future, fast reactors (U-238).
1.a. Per wikipedia [1]
Reprocessing the plutonium into usable fuel increases the energy derived from the original uranium by some 12%, and if the uranium-235 is also recycled by re-enrichment, this becomes about 20%
1.b. reprocessing in order to extract U-238 for fast reactors. That's a nice concept, but if we ever build fast reactors that can burn U-238 (fingers crossed), we already have a huge stockpile of depleted uranium. The US alone has more than half a million tons, and the rest of the world at least as much. That's enough to keep the lights on in the entire world for hundreds of years.
2. reprocessing in order to reduce the waste. That makes sense. But burying the waste is probably cheaper. We have already buried hundreds of thousands of tons of waste at WIPP. We know it works and it is safe. We know we will need to eventually bury some waste, even if its 30 times lower. If we, as a society, agree to open some deep geological repositories for nuclear waste, then it doesn't make all that much of a difference if we bury 10000 tons or a million tons.
[1] https://en.wikipedia.org/wiki/MOX_fuel
[2] https://en.wikipedia.org/wiki/Waste_Isolation_Pilot_Plant