If you have ever watched a deliver truck on their tracking app to crawl its way to you from stop to stop you realize the most optimistic timing is maybe 1 minute per package. Assuming the truck, driver, gas could be operated for 60 USD/hr the marginal cost seems more like 1 USD per package, but likely more.

No wonder Amazon decided to basically create their own logistic chain.

Fedex/UPS cost for a single package is roughly ~$13.95 (this was ~5 years ago when I was working in ecommerce) and even if Amazon was getting a huge discount from them for the volume they do, it was still probably nowhere near $1/package.