are you 100% sure publishers can set the price to $0? I've done some research on this, and I was under the impression that only Amazon can set the price to $0.
A quick google search seems to confirm that $0.99 is the cheapest price people can set.
You can publish a free book as an idependent author.
I have been annoyed by the occasional higher price of a kindle versus deadtree book. But often? That is a stretch.