My wife and I had this conversation the other day. Our kid is only two right now, but as we've learned, these milestones sneak up on you.
I used my own life as a guide to my opinion, and so landed on age eight or so. That's around the age I remember being able to go to the park or to a friend's house within the neighbourhood on my own.
Other questions about how much functionality the phone would have and how much access they would have to it at home are still to be determined.
Well, there's the fact that outrage seems to drive more activity than other types of content. YouTube sees it as a more profitable option to advertise a Very Angry Gamer(tm) to you, even if you aren't interested. I guess they assume that you'll find something to watch anyhow, but if they will profit even more of they can hook you into the outrage machine.
Then there's my personal hypothesis that in order to enable this, YouTube's algorithm weights your demographics, subscriptions, and viewing history much more heavily than your manual inputs.