If you have a preconceived notion that frames these questions in terms of privacy, then you will have a preconceived solution. Why is this discussion being framed in terms of "privacy"?
There is a large and growing advocacy for "children's privacy" that I am quite hostile to. The advocacy largely seems to be focused around allowing children to "experiment" and try things for themselves without feeling pressure from their parents to respond in a particular way, or fear repercussions. The stated goal is to let the child become their own person.
But by and large, these "experiments" are around topics like drugs, sexuality, politics, and religion -- and at increasingly younger and younger ages. All of these are extremely hot button issues, so I'll choose the last to make an example of. I've worked extensively through my church with our youth ministry. How would you feel if I wanted to have a "private" conversation with your grade school child about their sin, and necessity of repentance? If I responded to your objections by framing you as the unreasonable one, and asking why you wanted to invade your child's privacy? They need to become their own person, and be free to make choices for themselves!
You would be right to have a legitimate fear that your child would not be "becoming their own person" (as advertised), but being indoctrinated (or even brainwashed) into a certain way of thinking when their minds are too young to know how to appropriately think about these things independently. As a parent, no one should want to have "private" access to your children -- and even unsupervised access to your children should be completely transparent.
Freedom and privacy are important values to teach your children. But this is the privacy that should be taught: there are certain things that you should not expose to the world, and others have no right to ask of you. But the "privacy" that I see being discussed is an inversion of that. "We want privacy with your children, and you cannot violate that privacy!"
To close with an example of how I'd frame this issue: YouTube/TikTok wants unfettered access to my children, to sit them infront of a non-stop roll of advertisements, content that has been engineered to be addictive, and has the potential to create harmful feedback loops. To supervise, monitor, and restrict the quantity and quality of what my child watches (or even searches for) is not an invasion of my child's "privacy" or "freedom".