However I must disagree with you on the point of disallowing a single (unmarried) person to adopt.
While it's preferable for a married man and woman to adopt (because as you rightfully say, a child need a mother and a father), for some hard-to-hard-to-place kids, a married mom & dad couple is just not available. Married couples usually want to adopt perfect newborns. That's just the way it is.
Hard-to-place kids include older children (especially older boys), kids with disabilities, (especially ones that can't be remedied by surgery), and sibling groups.
What sometimes happens, is that a single family member will turn up (an adult sister, an uncle) who is willing to adopt. I would certainly rather have a kid adopted by an unmarried adult sister or uncle, than consigned to the purgatory of suffering known as foster-care.
(I'm not saying this to insult good foster-parents. I'm just saying kids in foster-care often get placement after placement that doesn't last long. This can happen over and over. This is emotionally catastrophic for kids.)
As I said, it's especially appropriate to have single-person-adoption if the adopting adult is a relative. But I would approve of it even if the adult is non-related, if the adult is mature and committed to providing a stable home.
I would exclude sexually-active singles no matter what their brand of sexuality. "Dates" or nonmarital house-sharers are at the top of the likely-to-abuse list.
I often think of the novelist Walker Percy, who, with his wo brothers, was adopted by their uncle, William Alexander Percy. It turned out to be a very, very good solution to a tragic situation.
I'd accept that a single relative should be able to take the child.