The atoms never leave the battery. There is no exhaust. It just works less well because it crystalizes in the wrong form. Which is a process that is trivially reversed.
I think they mean trivial compared to processing raw ore. The general assumption is that you are seeing the normal delay effects or inertia of the economy. Capital is already invested in mining and ore processing. Recycling needs to appear economically worthwhile for a long enough period for investors to grow interested and take the plunge in this new direction.
Note, I am neither a battery nor recycling expert here, but am somewhat interested in dragging unstated arguments to the surface!
I think proponents of this economic view of recycling often argue that you could mechanically shred/grind such post-consumer products into a big mess and think of it as a new type of high-density ore. It might take different refining stages, but they seem to have faith that industrial processing can be invented for these materials and that it ought to be less energy intensive than processing the very low density ores found in nature.