Let me preface this with with: No kid is ever going to fix your dysfunctional relationship, ever. At best, it's going to force you to voluntarily trap yourself temporarily in one.

That being said, after experiencing this twice among (the parents of) friends, I think that this quote should be amended to:

Having a kid to save your romantic relationship.

These were people who deeply cared for each other, but realized that their romantic relationships would either have a natural expiration date, or end in mutual disgust stuck with each other. But they didn't want to be completely separated from each other; they were good friends, both wanted kids, and knew that kids were the only way to ever be "forced" to remain together.

This however only worked because everyone involved always knew that: the parents were never, ever going to end up back together, and because everyone were civil and adult about it. The parents went on to have their own individual partners, the individual families remained civil with each other, and the parents were ready to never return to the dud of their former relationship.

It's not perfect, but a civil relationship between parents can work. And more than once, I've heard the phrase (with genuine sincerity) uttered "the best thing that that ever happened to our relationship was our divorce".