Last time I looked at it, maybe a couple of years ago, the parent's approach was not nearly sufficient if you don't want your phone communicating with Google. There was so much, including things baked into Android, that it would have been a full time job to identify and find solutions to everything. The only hope was another OS (including Android forks/ROMs), and none of those available at the time seemed sufficient secure - many didn't focus on security, didn't know what they were doing, or lacked resources to complete the job - or capabilities.
As one simple issue, I'm pretty sure Android uses Google's DNS and that is hard to change.
Sorry to be vague; I wish I had more details but don't have time to look them up right now. The basic message is: It's not sufficient, depending on your goals. to rely on settings in the GUI and to avoid Google applications.