Actually it's not trivial to change server APIs because they don't fully control all the clients (not even all officially supported ones). For example: push notifications are supposed to work without setting up a Google account (if you use a certain Android version). But if you don't log in to your Google account, you're not receiving updates through Play Store, and thus Google can't update the client. Google breaking their claim will upset some of their users (probably not the typical smartphone users, but think of entertainment systems based on Android for example).

Also note that most Google ToS don't specifically forbid third party usage (and some also specifically allow them), the only thing that's forbidden is to misuse APIs in a harmful way. Just another example would be the login/account management part of microG, that uses the publicly described OAuth APIs, obviously intended for third-party use.