I think you're underestimating the number of 3rd-party apps that use the Google APIs. This dependency is in no way restricted to Google-branded clients like Maps and Play - the APIs are required for the majority of behind-the-scene things, not least anything involving location (including in most OSM clients).

GNU/Linux-style package manager for Android is F-Droid, which bans apps that depend on Google's APIs. The effect of this policy can be clearly seen in the dearth of apps on F-Droid.