What constitutional problems? If marriage went back to where it was as a religious rite, then the Constitution has nothing to do with it. Furthermore there are a lot of people like myself who never wanted to be married so I never got married. I have lived with a woman and children on several occasions. The only way for us to get marital benefits would have been for us to get married, and those women (like myself) objected to any kind of marriage religious or otherwise.
Unless you are planning to have children to carry out your name, marriage to me is stupid. How does that conversation go anyway? "Honey, I love you, and you love me. We have this great thing going, and the only possible way to make it better is getting government involved in our relationship!"
So a social contract replacing government marriage preserves marriage for normal people and gives anti-marry people like myself the ability to have the government benefits married people get.