This is another argument balanced on wobbly undercarriage.
Stats say that married people more likely to stay together than unmarried. I believe this is true, although I do not believe the statement in the OP is true.
So people hark back to the days when people all got married and divorce rates were very low as some kind of "golden age". Forgetting that the reason everyone got married was social convention, and not always for the right reasons by a long chalk. (shotgun weddings etc). Then there were no divorces also because of social convention, and women were tied to men financially. So many childen being brought up in married families which were deeply dysfunctional violent abusive etc etc.
Then feminism happened
Women no longer had to stay with men who were shits, they gained a certain amount of financial independence, domestic violence and other types of abuse were recognised, divorce rates shot up.
Roll on a society change where being unmarried and having children is no longer stigmatised. Now that people are no longer forced to marry, many don't.
I would argue that the basic relationships have not changed. It is simply the labelling that has changed, and society attitudes towards marriage. Some relationships are strong, some are weak, some are one nighters, some people are unfaitful etc etc. Nothing is new there. What has changed is that when people are shackled to a shit they can leave, and that they don't have to get married for society to recognise a serious comitted relationship.
People who say everyone should get married are effectively saying that women should put up with a lot of shit in order to adhere to outdated social construct.
The stats for more married couples staying together are easily explained by the fact that now marriage is truly optional, generally it is only the most sure and the most traditional who do it - the types who would be likely to stay together anyway. The act of marriage itself is irrelevant. It does not imbue relationships with magical properties.