Can somebody give an example of a service that needs this, where Fedex wouldn't do?
The local delivery case is really where UberRUSH provides the most value. We also take pride in our developer tools and experience and invite you to check out our docs: https://developer.uber.com/docs/rush I'm curious how you might compare them to FedEx's docs? http://www.fedex.com/us/developer/web-services/index.html
As an example, the developer document solely for obtaining shipment rates is 98 pages long.