There are many excellent applications (DevonTHINK, etc.) that allow you to import PDFs with highlights and notes so that they can be organized there. Every other PDF annotation software maintains a layer for the highlights and notes that travels with the PDF so they can be imported together. It would be great if we could export the PDF from Papers with Annotations - this seems like basic functionality that his missing from the app.
Implemented in web and desktop app. Just hover over the download PDF and you should see options to include your annotations.