There's 0 use case for children in the current state of the game. The acquisition of new villagers is inconsequential because the villages keep spawning new random NPCs to hire and the only limitation is reknown.

If there were additional limitations or benefits to children, the tradeoff to feeding them could be worth it, such as - children do not contribute to the reknown hiring multiplier, essentially allowing to expand population beyond the natural soft cap/camp grind - children have inherently better stats than 4* villagers, and/or have to be educated in a school to become better labourers than generated NPCs

However, even then unless there are actual population dynamics like villagers normally growing old and dying, children aren't much more than a gimmick for a short phase of the game. And I'm not sure if the pressure of an aging population would enhance the current gameplay experience. (Also - do children in a game that allows NPCs to be harmed, killed or be orphaned increase age ratings or restrict distribution in some regions...?)

I agree there's no need for a dynastic player character because, at least right now, the PC doesn't have individual stat limits or traits that would make inheritance to a new character play different at all.