If everyone is a parent of a child, then no one is? I can also imagine how confusing divorce proceedings will become with four, five, or six people claiming to be the parents of a child. Is the state going to amend and expunge birth certificates over and over to update them for new parents? With more than two parents, which one would be accountable? How would custody work between three, four, or more people. You couldn't throw kids into a different home every day of the week, it would create instability in the child so that they no longer understand what a traditional family really is, but I guess that is the point.
The government thus becomes the real parent, the real parents lose much of their parenting rights, and the real concept of family is destroyed. There will effectively be no restrictions on the government's ability to raise, coerce and indoctrinate children to the government's ideological agenda. Who needs to worry about elections if you can program the electorate with your ideological views from cradle to grave?
Absollutely!
Think about the growing federal programs providing meals for children at schools - even in the summer when schools are not in session.
They are gradually conditioning children (and parents) to look to the state as the primary caregiver.
This helps explain the enmity shown to homeschoolers.