There isn't much that's good to be said about any form of plastic packaging, but at least the peanuts are imminently recyclable; you can use them again and again and again. Shredded paper can be composted, so it's not a great problem.
I take the peanuts to work. I work in a small warehouse from where I despatch a variety of items every day. Some, like CD jewel cases, are fragile and we can't afford to purchase large amounts of packing materials, so I recycle as much as possible. All incoming plastic wrapping, shrinkwrap and even the vile pallet-wrap are screwed up to fill holes in outgoing parcels.
The very last place i'd put them is the garbage.
GG