I saw a show (either 'How it's made' or 'How do they do it') about batteries. They showed that many batteries use a thin lead mesh that is covered in a paste of other materials. I don't recall what they were, but I don't think they were lead. Cadmium?
But then again, on that same show they had a warehouse full of batteries and a loader driving around in an indoor lake of battery acid scooping them into piles for grinding, some of them were sparking. They ground them up, separated the plastic out then smelted it into clean lead ingots (big ingots). So, evidently on an industrial scale it is do-able.
Prior to this, about a year ago, I tore apart a lead acid battery from a computer power supply. It contained crumbling nasty junk and was a waste of time.
People tried to tell me, and now I know.