Earlier quoted context omitted.
No, you misunderstand what the logic here is. Parents should be able to consent to some things in the name of their children and absolutely should not be able to do it for other things (even those things their children would be able to consent to were they grown ups, so I don't mean illegal things). Exactly what stuff the parents can consent to is the real question and should be argued properly and not treated as any…
I perfectly understand the logic. Data processing is ubiquitous these days and control and consent falls well within what parents are there for. That is common sense: parents are there to make decisions on behalf of their children on issues children cannot handle.
Well (as you said - and thankfully) not any more.