derefr cited one reason but there's another that's relevant to this thread: updates. In the Android model handset manufacturers and carriers decide when (or if) to ship updates. Google distributing their apps through the store gives them a way to roll out new features to a reasonable portion of their user base.

Google can harvest data from "virtually all Android devices" just by offering Chrome, Google Search, and Gmail as apps. Almost every Android user has at least one of those apps installed. They don't need Play Services itself to spy on you on top of that.