Start with all the reviews people write for Amazon (including myself.) No way Amazon should be able to legally claim these as its exclusive property; yet right now this review pile is probably their most valuable asset.
Similarly, Google quality is in big part due to invaluable information of what URLs were clicked for what queries.
If duckduckgo had access to that information, their quality would've been way higher, and there's no reason I as a user shall not be able to give access to the information I generated for Google to another service.