Yes, we all want a battery to be recycled, but recycling batteries is an arduous task that cannot be automated efficiently in any way. No company will spend the man hours on recycling batteries if they're not forced by law, because it's a terrible cost sink. Even with recycling the material gains from taking apart batteries are terrible.
Extracting lithium from a cell is damn near impossible, but the other metal parts can be metled down, so my guess would be that when a large amount of batteries reach their end of life, they'll just be burned and molten, possibly with some filter attached to the smoke stack that'll do the absolute legal minimum to protect the people and environment from the toxic fumes.
Or, what might happen is what has happened to plastic "recycling", we export the stuff to third world countries who offer to "recycle" the stuff for cheap, where they'll just end up in a landfill, waiting for the occasional fire.
Sure, these companies tout that they're going to recycle all of these used batteries right now, but in the end I have very little faith that they'll actually give a damn about recycling. They're not even recycling used cars for more than their metallic elements, so why would we ever believe that they're going to recycle something as complicated as a battery pack?