The anodes and cathodes of the cells tend to acquire a film of lithium and electrolyte oxides which reduce the coulombic efficiency of the cells, i.e. it makes it harder for the electrons to interface between the anodes and cathodes. I don't see a reason why we cannot extract the lithium from old cells for reuse, other than economic efficiencies of fresh lithium supply versus the cost of sorting, unpacking, and extracting from old batteries.