It seems like it would be impossible to prevent bugs and rodents from getting into packages in facilities that process packages if there was this much free food available.

This is the main issue with things like popcorn and other foodstuffs: Insects and other pests truly love it. Suddenly, you have an insect problem in places that don't have food.

Perhaps it might be feasible were the goods properly sealed? I feel like it would require every step between production to shipment which would require clean environments- that might not be necessarily cost effective, but it is definitely an interesting idea. I would certainly prefer that all packaging be substituted for nontoxic sustainable and compostable materials- it seems doable, additional steps notwithstanding.

Packing peanuts are often made out of corn starch. The problem is how the packaging comes from the receiver to a sensible use.

And these are totally edible! I've popped a bunch in my mouth.

I've had stuff delivered to me packed with actual pop corn. Don't remember what it was, but a small object.

Indeed - the packing peanuts use case and styrofoam use case are very different! Former is already solved by starch (dunno why polymer peanuts still exist, maybe we should ban them), latter seems a great deal harder, that's the claim made in OP's link.