Theory: Babies are Wishes Granted by the Stars

Abstract
Babies in the Mario universe come from wishes from parents, granted by the Stars.

Arguments

 * Argument 1: The 7 Star Spirits have the job to grant the wishes of good people. When those wishes are granted, they transform into shooting stars and land in Star Hill. Some of the granted wishes in Star Hill include having children, meaning that the Star Spirits are capable of granting these types of wishes.


 * Argument 2: In Yoshi's New Island, it's revealed babies are created in a land way up in the sky. Star Haven, the home of the Star Spirits, is also located way up in the sky. Both locations being high up in the sky makes sense if the two are connected.


 * Argument 3: It's not just Mario & Luigi that are carried by stork. In Yoshi's Island DS, many children of different origins are seen to be carried by storks, who all know where to deliver each child. The fact that the storks are acquainted with where these children are supposed to go supports that these children were also created in that magical cuddly land, seeing as storks come there to pick up children.


 * Argument 4: All new life carries the essence of stars, as revealed by Rosalina in Super Mario Galaxy. Combine that with the previous arguments, and it's likely that this essence comes from them being created by the Stars.