Worse, it's a relatively minor manifestation of the broader notion that the child has a fundamentally lower status in the family just for being a child, that they deserve less weight in the family's utility function.

Are you sure those two are the same ?

In Chinese traditional culture, children are explicitely of lower status (they need to be respectful and obedient etc.), yet families will make great sacrifices to be able to afford a good education for the kids. So it's possible to be both at low status and have a big share in the "utility function".

I don't see what's wrong in itself with children having lower status - that seems to be the way humans have always worked (seems nearly hard-wired!). Sure, there are ways to abuse that power difference, but that's another issue.