It is hardcoded to access the Google app, and if you remove the Google app, it just shows an error.
There are several such cases.
For example, Doze will terminate all apps – except for Google Play Services’ GCM service, that one can stay. This is, again, hardcoded.
The only way to modify these things is by actually recompiling SystemUI.apk and framework.jar. Which no normal user can do.
Google has to treat all competing services the same as their own on Android or Search – in general, in all markets where they have a majority.
Microsoft had to add BrowserChoice.eu, and Google will have to add the same for Android, too. Microsoft was prevented from forcing OEMs to install Windows everywhere, and Google’s Anti-Fork Anti-Kindle clause will be declared invalid, too.
This is the law, and if Google wants to avoid doing so, they’ll have to avoid operating in the EU.
As long as Google forbids OEMs from producing both FireOS and Google Android devices, I can’t buy a CyanogenMod device from Motorola, or similar.
And no, I don’t think Google should be able to hardcode any of their services into Android – instead each service should be provided via a standardized API, so users can select defaults (like it already is done with many apps on Android).