Things like https://en.wikipedia.org/wiki/Creole_language and children of immigrants often not learning their parents' language well make me skeptical of the importance you're assigning to parents as teachers.

There's many a motivation for a parent not teaching their native language to their children -- my step-father's parents didn't teach their kids Spanish because they didn't want them to have an accent (and also got beaten as children for speaking Spanish in school as that was the '30s rural New Mexico way).

Don't you think the bigger lesson from that data point is that immersive learning takes a lot more than 3 participants?

While your comment about people picking on education does hold true, I don't think the way the child learns from her parents is similar to what is done at school. Here, the child tries to speak on her own and gets a lots of feedback from her parents that help her get better at it.

If you haven't read any of John Holt's books, they might interest you.

Exactly. I remember reading in an introductory linguistics book (Fromkin's, I believe) that a linguist once conducted an experiment with his child. The kid kept saying "I want other one spoon!" or something similar. The linguist was able to get the kid to say "another spoon" perfectly, but then when he told the kid to say it all the kid went right back to "I want other one spoon". He just hadn't intuited all the rules yet. Basically, L1 acquisition is just that -- acquisition; it's not really learning in the sense we think of it in terms of L2 and other subjects (though, of course, learning the standard at school is an entirely different animal).