I read a first-year Canadian psychology textbook about this topic. It had two interesting points:

1. Children raised by a two-parent family had more life success than children raised by a single parent or estranged parents (in general).
2. Couples who got married were more likely to stay together until their children were adults than couples who were cohabiting (in general)

I can’t remember the exact statistics, but there was a very significant difference in the outcome of children for marriage vs. cohabitation.

And it didn’t seem to matter whether the marriage license was issued in a church followed by a big wedding or by city hall with a couple of witnesses. Something about that legal paper kept couples more together.