This is a cute idea, but there are several things that might cause SE to scrap the idea like:

1. Who is to take care of the child when you're not at the house? ( could hire an NPC babysitter maybe)
2. What happens if you and your EB partner split up but both want the kid? What happens to the child?
3. What do you do when the child grows up?

There is also the problem that with the way character customization is, that most males can look like old men. Now, some might find it funny but then there are those who take to roleplaying their character's age seriously....so...yeah.

Again cute idea but SE probably wants the players to have their characters focused on saving Eorzea than raising a child.