You say:-
"A parent's "right" to parent is supported only to the extent that it meets the right of a child to BE parented, otherwise it would be an unfair imposition on the rights of the child. So parents' rights derive directly from, and are contingent upon, the child's interests and rights."
We've done this to death already, but if the child's interests and rights are all that matters then what do you do about the parent who abandons their child? You may get money from them to support the child, the state does that of course, but you cannot turn that parent into the good parent the child needs. You can replace the parent, if necessary, or you can allow the other parent to give the child what they need to meet their interests and "rights to be parented" as you would have it, as far as possible
Unless we are going to allow children to die when abandoned by their parents that is incumbrant on the state to provide in the name of the people.
We parents are human beings who make mistakes in the course of our lives. We need the state to protect us when the other parent wishes to deny us any involvement in our child's life. You would hold that the child needs the state to uphold it's interest/rights by preventing one parent denying the other any parenting time. But the child cannot talk when it is born, may express it's hatred for one of it's parents and so on.
If all that matters (I know absolutist terms again) is a child's interests and rights what do you do about children hating a parent? I know you say you will make the courts deny them as children whatever it is, the authority to reject a parent or however you desribe it, because you will tell them it isn't in their interests and so on.
If I provide you with care as my child, and yet you owe me nothing as a parent for doing that, because quote: "parents' rights derive directly from, and are contingent upon, the child's interests and rights"......then this is "unfair" too!
The child owes the parent who treats them well respect, or even love, and our family courts need to be able to recognise that fact and tell the child so (and tell the ex partner the child owes the other parent these things).
We will not agree of course, because the views you are giving us all here are strictly establishment opinions that aren't going to change whatever we might say.
Keep fighting Frank, for all those authoritarian bodies and institutions who will be applauding you all the way.
All the best, Graham