I'm not talking about the Google Maps app or the YouTube app here. I'm talking about the API's which Google Play services offer which all apps use. API's which for example allows your app to get the location of the user. Or allows your app to be updated.

Simply said probably none of the apps you installed on your phone are going to work without Google Play services installed. Google Play services are closed source. Which is why manufactures like Samsung need to sign a contract with Google and can't simply "install opensource Android". Samsung could live without Google Maps being installed and they could even live without the Google play store but they can't live with none of your apps (like your bank app, your Netflix app, etc.) working.