Importantly, this is a reasonable thing to do because sites like Youtube are designed to draw their attention away from whatever important thing they're doing so that Youtube can serve them advertisements. So anyone thinking a parent trying to control what their kid watches is oppressive somehow is pretty deeply in the wrong. As a parent myself I would consider doing this to keep my son from falling into the traps that are set by giant multinational internet companies like Google to get him to form habits around Google instead of habits around what he wants or needs out of life.
So really instead of thinking about this like "parents are acting like nation states" I think it's much better to think of it like "parents are countering corporate nation states."
It's totally reasonable. My position is that I think network operators and owners should be able to do that they want. I was just pointing out that virtually any time a network operator or owner wants to control the traffic in their network a certain crowd comes out of the woodwork and decries abuse by bad actors.
Size and scope matters. Large network operators that have a de facto monopoly on Internet access in many places should absolutely not be able to do what they want, but this is a function of their market power, not something inherent to any network operator.
So really instead of thinking about this like "parents are acting like nation states" I think it's much better to think of it like "parents are countering corporate nation states."