Be careful next time you buy or shackle yourself to a new phone, it will probably have an unremovable FB app. I see no reason why it would need you to have an account to track and analyze you.
This is why it's so important that open source forks of Android are available. Without them, it's not possible to have a modern mobile communication device that you can actually trust. (Arguably even then, since drivers tend to be opaque blobs and the radio subsystem runs its own closed code, but at least you're no longer free real-estate for any application big enough to pay for an unremovable app.)