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.