The idea that fatherhood redeems men, turning them into proper grown-ups (and thus acceptable members of society) is an enduring pop cultural preoccupation.
In Three Men and A Baby, the lead characters are living in New York, having fun while still (more or less) covering their bills — but it takes raising a baby and giving up wild parties to validate their existence. Jack, baby Mary's biological father, is the most irresponsible at the start of the film, and the one who is most changed by the experience. In case we missed this subtle lesson, Jack's mom makes it explicit, informing him: "You used to be a screw-up. Now you're a father."
Conveniently for writers, a man doesn't need to have spilled some sperm to have his formerly worthless life transformed like this. For Charlie Salinger in Party of Five, it just took his parents dying in a car crash. Suddenly, this 24-year old slacker who made his living from odd jobs and had a different girlfriend each week was in charge of his four siblings, who ranged in age from one to sixteen.
I used to love My Two Dads. To recap, or in case you (shocked face) never saw it: the show was about two single, straight Manhattan bachelors who were given joint custody of 12-year old Nicole after her mom/their joint ex-girlfriend died. Living with just one mom, I was fascinated by a show that centered around a girl's relationship with her two fathers. Except I re-watched some of it recently, and it's not about that at all.
I don't have exact stats, but it seems like the vast majority of shows and movies about single and stay-at-home dads feature a father-daughter dynamic. This could lead to some interesting explorations of what it means to parent a child with a different gender to your own in our patriarchal society. But most often, it's a way to reinforce society's discomfort with young women's sexuality.