Not to defend the shipping or business use of plastic, especially not Amazon packing practice, just to get this out of way fisrt.

In general, consumer plastic waste are almost not recyclable. It cost prohibitive to clean the plastic from consumer waste in to useable state, a lot of recycle stuff you put into the blue bin eventually goes to landfills. So cutting consumer end reduce overall wastes going to landfill/burnt, by a pretty big percentage. (Like stop buying individually packed cookies or candies) Believe it or not industrial use of plastic stuff isn't that much and they are cleaner/easier to recycle. (Ie, the pallet wraps someone mentioned are much cleaner than your bubble tea cup/coffee cup caps. I do not know if there are similar strength/durable retention materials that can replace the pallet wrap, that's a different issue.)

Plastics are not "evil", they are flexible, durable, light weight, and above all, cheap to manufacture and alter. (Imagine all you containers become stainless/glass, and carry them for picnics or travel) many products are reusable as well. So targeting single use is a good start, that include shipping fillers. Things like air port luggage wrap or pallet wrap can have designated area for recycling the material, or tracking the waste by weight to make sure they aren't just throw to random dumpster. 20kg wrap on to the shipping cargo, 20kg of wrap needs to be collected at destination. I know not all pallets goes to the same warehouse, but the idea sticks. If we can track stuff like individually packed micro SD cards, we can track pallet wraps.