you say:
"this is in opposite to "live in" relationship wherein the couple is not binded by any law, no responsibility at all,be it personal or social, instead they'll create a problematic society."

What kinds of problems do you envision these people in relationships unbound by law creating?

I know plenty of unmarried couples, some who have children together and have been a couple for decades, and they seem just as happy as the legally married couples I know. In fact, they often ascribe the success of their relationship to the fact that they are both free to leave at any point.

I'm not saying that this is better than being married, but I don't think you can assume that people who are in a relationship like this don't have any responsibility towards one another, or any sense of commitment. Many of them do, often more than married people.

"Most plain girls are virtuous because of the scarcity of opportunity to be otherwise."
-- Maya Angelou