@Christoph_Ortner the way I worked around the limitation is to synchronize Paperpile Google Drive folder to the computer, and configure Mendeley to watch that folder. This way you have full functionality on the desktop - search, read, annotate, generate citations (sans ability to use Paperpile in Google Docs offline mode), you have a very capable app on your mobile platform (Paperpile mobile app is nowhere near the one from Mendeley), and when you are back online - you can use Paperpile just for Google Docs.
I think it will be hard for Paperpile to compete on the desktop and mobile fronts. It would be interesting if they just established some partnership with Mendeley, and focus just on refining the Google Docs features.