Obviously, you will be able to find plenty of examples of things that don't work, and you probably have a bank app or some other thing that you need Google for, but alternatives do exist, and I'd argue that you can have a healthier, more productive, and more enjoyable experience if you can have all your needs met by software that isn't treating you as a product.
My opinion is you should use whatever works; I do. But try not to absolutely need software that you can't control.
Some countries have tied their banking to their phones, with apps that use SafetyNet to check how Googled you are.
Somehow corporations and nations have given sovereignty away for convenience and so you may need 2 phones: the google one and the good one, to properly be f-droid only.
Makes me wonder what the tradeoffs/alternatives are. Maybe they could have still moved features to a Play Services-esque library but published the source for it. Considering we're commenting on a post about how developing in the open is too inconvenient for modern Google, the difference might have been moot.
AOSP is a compromise, because device manufacturers don't want to share anything. Google effectively negotiated with device manufacturers to open source part of their software. Device manufacturers lose some of their secret features to competitors. In exchange, they don't have to develop those features themselves. App developers get a standard platform, which benefits everyone: users and manufacturers and app developers.
This is very much a win-win situation, because the alternative is that every manufacturer has their own proprietary system.
No, it's a lose-lose situation. If we have 100 different mobile OS's it's a matter of time until a "good one" appears, and we get some sort of innovation in the space - be it from a technical perspective, from an UX perspective, or whatever.
Now we're all stuck with Android, where manufacturers can't really do anything interesting with their phones, users get an incredibly bloated, technically incompetent system, and all parties have to abide by Google's every whim.