The percentage of cobalt in modern lithium ion batteries (ie: tesla/panasonic's nmc-811 cells) is only 8% of the battery material. It's almost entirely Nickel now (72%) with traces of manganese (8%) and cobalt (9%). Even the lithium percentage is down to ~11%.
I was under the impression that the biggest issue right now was scaling up recycling facilities and recycling pathways back to those facilities so that they can handle the huge influx of batteries anticipated in the next 3-4 years. I don't think recovering 97% vs 95% of 8% of the material is going to change the economics of battery recyling.
The more interesting breakthroughs seem to be low-temperature, safe-chemical extraction. Let's not forget the advancements in cell composition that will lead to longer lifespans (2-3x higher cycle counts) - which not only reduces the waste from battery packs but also that from devices that use them.