Google Play Services offers a lot of baked functionality many apps have come to rely on.
That's true. However, just like any other third party library, app may use, but they don't have to. It is up to the developer. It is perfectly fine to develop Android apps that do not use Google Play Services.
In fact, if you want your app to run on Chinese devices or Amazon devices, for example, you have to account for missing Google Play Services.
Especially because the Google services run on the Google servers and you have to contact them in order to use them. The same is not true for just using Android. However, the thing regarding Google services is true whether you use them on Android or any other system.