This was from speaking to an expert, but from what I recall recovering plutonium is perfectly reasonable trying to recover the uranium isn’t helping.
First you don’t actually reduce the number of atoms of highly radioactive waste products. You’re simply chemically separating material not transmuting it to something non radioactive. Which doesn’t really make the nasty stuff easier to deal with.
Second, you end up contaminating a great deal of additional material which then becomes a high volume of low level radioactive waste. At the same time you need an input stream of various chemicals, steel, rubber, etc to replace what’s been contaminated/used which then causes environmental harm when you’re extracting them.
Finally plutonium is useful as fuel, but the ratio of u235:u238 changes so you still need enrichment. Which means at the end of this process you’re spent a great deal of effort only to throw away most of the uranium recovered.
There are reactor designs that don’t need enrichment such as CANDU, but they need far less raw uranium mined in the first place.
TLDR; What you’re recovering is u235 which is a small percentage of spent fuel and it takes a huge amount of resources to get at it.
How so? Any pointers for more info - I'm somewhat ignorant on this topic.