Overwriting most core OS files (eg. shared libraries) in a persistent way, even with an exploit, would be difficult since the entire /system and /vendor volumes are signed using the device manufacturer's dm-verity keys.
However, with Android 10+ shipping with APEX modules [0], Google's ability to push core OS changes to existing devices might be changing. I'm not sure if any devices ship with the unflattened (ie. updatable) type of APEX modules yet, but I'd suspect these would be signed by Google instead of the device manufacturer and would be distributed through Google Play.
The move away from developer signing towards Google's signing will makes it harder to detect such event.
Even if one OS component (Google Services) is centrally controlled and can be used to attack you, this does not mean, that you should make other parts less secure. Real-world attacks are complex and backdoors are fragile and prone to being detected. Embedding a backdoor in proprietary code of Google Services is easier than embedding it into AOSP. Hijacking a specific application is easier yet.