Agree. I had a free app with 100000 downloads, no ads and 4.5 rating on Play store, it is no longer there because I got fed up with Google's nagging. If I will do free things going forward, I will do them outside closed ecosystems.
It is economically better for google if your free app is gone and someone makes a paid app or an app with ads...
Interesting point. I think that the availability of good free apps on Play Store has a positive effect on the market for Android phones in general. I know it factors into people's decision of phone religion that apps are more likely to charge on Apple's store (even sometimes for an app which is free on Android).
All that said, F-droid is the only one I'll ever love.