Marriage is a sign of stability.
I'm sure there have been studies showing just about everything. It depends who paid for the study, doesn't it. When little Sally's having girl problems, either one of her dad's ain't gonna be able to handle the situation. Same with little Johnnie and his two Mom's. That's just plain common sense.
I'll give you some examples. My wife is a very intelligent person. Her IQ is nearly as high as mine, but she has a memory that I can't begin to match. She's got professional training and experience in Psych. Sometimes my son does something that she can't figure out at all, but when she tells me about it, I instantly know how to handle it. The difference is that I've lived through it- I've been there. Sometimes my daughter does something that completely stumps me, and I hand her over to my wife, who has a completely different perspective.
These kids deserve the best that society can give them. And the best always involves a stable, married, heterosexual couple.
I think your stats ignore the fact that there are kids going into the system and coming out at the same time.