I completely agree with your comment, JLZ. As Lou Lou has said before, it is not about the rights of a parent. It is about the rights of a child.
It is not so much that a parent has the right to see/contact/care for a child, it is more that the child has the right to see/have contact with/be cared for by that parent. And when FACS has to intervene, the child's rights with that parent may be circumvented.
Every single thing that I search for regarding parental rights basically comes up with the rights of the child/ren.
As you have said, Family Court abides by this way of thinking as well. It is enacted in law.
"The Family Law Act 1975 focuses on the rights of children and the responsibilities that each parent has towards their children, rather than on parental rights. The Act aims to ensure that children can enjoy a meaningful relationship with each of their parents, and are protected from harm."
https://www.ag.gov.au/FamiliesAndMarriage/Families/ChildrenAndFamilyLaw/Pages/default.aspx