Paper is an organic material with structure. Recycling damages that structure when actually you want to preserve it as much as you can. At some point you need a tree to grow to put that organic structure in place.

Batteries have human made structures constructed from pure materials. Battery recycling completely shreds the batteries and then mechanically & chemically separates the materials giving you the pure copper, gold, aluminium, cobalt, zinc, etc back. You're then back to step 1 of the manufacture except you didn't mine your raw materials.