Or... it requires you to use the parental controls built into the phone OS (which it loudly insists you set up if you're setting up a phone for a child) to whitelist what apps the child can even be accessing, to only be ones you have the time to understand.

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To be clear here — and maybe this is a miscommunication in this conversation — when I'm talking about monitoring the online activity of "children", I'm talking about e.g. six-year-olds. Kids who are at a young-enough age that they don't yet have a mental schema of the world that includes a term for "online sexual predators." (And yes, six-year-olds these days have smartphones. Or at least they do if they take the bus to school, do any organized sports, live back and forth between divorced parents, or one of any number of other things that create the possibility of an emergency where they're stranded somewhere and need to be able to reach you. Pay-phones don't exist any more, remember?)

I don't think monitoring the online activity of a six-year-old is a particularly difficult problem, because it's not adversarial in the way that monitoring older minors would be be. Six-year-olds really just don't have that many things they want to do online; even the ones who are heavily absorbed into screens, are mostly passively consuming content or playing games. They have no impulse to create social-media accounts and profiles describing themselves in the way teenagers do. (There's a clear through-line from going through puberty and unlocking the "hormone production" part of the human tech-tree, to wanting to be seen as socially impressive, to oversharing on social networks.)

Meanwhile, I don't think parents should bother trying to monitor their teenagers' devices at all. For two reasons:

1. If you have a healthy communication channel with them, and you explain what the risks of engaging with strangers online are — and if they also have no reason to actively seek out adult attention (i.e. if you aren't neglectful/abusive) — then they will do perfectly well protecting themselves. Their mental schema of the world does include a term for "online sexual predators" — trust me, it does, even if you have never personally explained the concept. They might have ill-considered reactions to such threats — e.g. deleting messages that gross them out instead of saving them as evidence, or capitulating to (what are to you obviously bluffed) threats of blackmail — but these are exactly the sort of practical micro-skills that make up the modern version of "educating and socializing" someone.

2. It's just a losing game to try. Unless you literally never let a teenager leave your sight, they can work around literally any restrictions you try to impose on them. And not just by nerding it up with jailbreaking or what-have-you. If you give a teenager a locked-up/monitored phone, their most likely response will be to treat that phone as a decoy, and to ask a friend at school — one without helicopter parents — for an old used phone of theirs (everybody has one) to secrete away and use as their real phone. Then, the first time they get a spare $20 in cash, they'll walk into a convenience store and get a prepaid SIM card for that phone, so that they can ensure it never touches your house's internet. There is literally nothing you can do to stop this (that wouldn't make their life worse than that of most maximum-security prisoners.)