I think it is a Slippery slope when it comes to legal reasons. All it takes is some Child (Minded) person to do something distasteful with an NPC child, to cause a huge amount of damage to both the image of STO, and it's player base.
I would love to see children in ESD, on starships, and otherwise, but I am afraid of what "Some" people would do.
Anyways, I don't think not seeing children detracts from the game. Maybe if we get to go Starfleet academy then we should see cadets, teenagers or young adults, but unless there is any particular reason in a mission, I would have to say no to this.
There was a group of children in Tabula Rasa, but they were alway in a group with their teacher on a set patrol path. Maybe Starfleet and Klingons has done away with children or let them stay in Maturation chambers for a few years until they are ready for the work force.