I suggest a new monetization strategy: integrate code to collect useful scientific data from the phone's sensors in the background. This data, in aggregate, is potentially valuable after being anonymized, cleaned, and re-packaged (by a third-party). App developers could make partnerships with companies who need this data - both parties can benefit through revenue sharing.

An example of how this might work: I run the PressureNet platform, which collects atmospheric pressure data from Android sensors. I wrote a library project that you can drop into your app that handles all the sensor data tasks. App developers can integrate this code and join my weather sensor network; in return for sending data, any profits in the future can be shared among the contributing apps. Does this strategy seem viable? Would you consider adding a similar library to your app?

http://pressurenet.io/

https://github.com/Cbsoftware/PressureNet-SDK

[1]: The Majority Of Today’s App Businesses Are Not Sustainable: https://news.ycombinator.com/item?id=8092518