One of the comments that resonated with me, though I certainly don't think the issue is limited to polyamorous relationships, is the issue of disappearing adults in a child's life. I experienced the same thing with my uncles-in-law, bonding with them only to have them disappear when my aunt divorced them. There was no legal obligation to allow us to spend time together. This felt like a constant replication of my abandonment by my father. I think that there ought to be some thought given to how to handle this in a way that doesn't leave children repeatedly living through this kind of loss--whether in monogamy or polyamory.
Otherwise I have nothing against polyamory. Like any other form of relationship, it needs to be practiced in a careful and thoughtful manner.