As for the patriarchal connotations, I viewed surrogacy in the same bracket as fertility treatments and adoption. Things that enable people who couldn't have children, to have children.
Well, the enabling of people who cannot have children to have children is basically what patriarchy is about.
Fertility treatments help people who in principle can have children to make use of that potential.
Adoption should be a way for children to have (good) parents, not the other way round.
Men cannot get pregnant, i.e. cannot "have" children in a natural way. Schemes to test the genes of a child and then inform the biological father and then give him rights over the child, are all cultural. Being chosen as a partner for child raising is the only natural way for a man to "have" a child.
Patriarchy is basically a way to ensure that men get to spread their genes without the consent of women, and that they get to own the resulting children, shape them to their will and kill them off if they want, again without the consent of the mother.
Which is I am not at all in favour of talking of a "right to have children."
What people should be entitled to through the NHS is a body that's as healthy as possible, and this health includes the natural reproductive capacity of a body. Infertility is often the result of a disease, injury or poisoining, and people have a right to have the capacities of their body restored.
But no one has a "right to have children" - that's a very patriarchal notion.