Just a random musing, most people say having baby can save a failing relationship. I have never been able to understand this. Is it true, does that work?

Disagree strongly. A newborn brings tons of challenges. Sleep deprivation, post natal woes, financial toll, etc. All this, couple with factors that the couple would be tired and irritable from the lack of sleep can take a huge toll on the marriage. I am one good example - less than a month after my son was borned, I filed for divorce for infidelity.