I could see that for sure. In a modern world where each family is isolationist the idea of a larger nuclear family that can replace the village it used to take to raise a child is interesting.
But with childcare it isn't always about checking the boxes. Kids are weird like that, you can provide for all their physical needs and still do them harm via not meeting their emotional needs.
One thing that is HUGE for children, and that helped gay marriage, is that kids thrive on stability:
http://www.urban.org/UploadedPDF/412899-The-Negative-Effects-of-Instability-on-Child-Development.pdf
I will be honest that I don't know how it actually works in a poly community, but with so many "parents" coming and going the situational stability might be lower than in a two parent household. Even if a bad mom who gets married and divorced three times is no better in the stability department doesn't mean that people will sign off on legalizing more situations like that.
Or maybe a poly household is more stable because the relationships last longer than your average marriage, I don't know. I could see it going either way. No matter what though this concept of stability has to be addressed before many people will see a poly household as a suitable environment for children to be raised in, which is the path to legalized marriage That is where some more research could really help.