There are good reasons for bringing back the scarlet letter. By engaging in sex with someone who is married you risk bringing into the world a child who will not have the possibility of having a father. Especially if that father has children with his spouse. The problem becomes one of punishing the wrongdoers without harming the innocent children. Not an easy task. Marriage, though, is a contract and the State is a party and the purpose of which is to provide for the rights and welfare of the children produced. If that contract is violated, civil penalties should be imposed. The harm done to citizens by children of broken households (the jails are full of them) raises the question of whether criminal punishments should follow as well.
If cohabitation results in children, the parents should be considered married by "common law" as well.
This is all proof-positive that the government should get entirely out of the marriage business.