The laws that are being complained about have nothing to do with getting married or getting divorced. They are all about establishing who is the legal parent, and thus responsible for support of the child.
You have to remember that most of those laws were written long before current dna testing, etc..., came about, so there were intricate laws designed to establish the burden of proof associated with who is the father of a child. If the child is born during the marriage, or perhaps within a defined period after, the husband is presumed the father, and in order to avoid support obligations, must overcome that presumption. If the child is born out of wedlock, the burden shifts.
That's what those statutes are about.