Another idea would be to have a regularly scheduled new arrival event. We already have those. Just make them pop up much more often, so that players can rely on it happening. Maybe there could be refugees regularly arriving from another part of Isola where it's harder to survive. Don't most of us really like the canoe and barrel of babies events?

Here's an idea to solve the "random embracing" while the player is not looking: Just make it so autonomous embracing can only happen if BOTH villagers are set to Parenting. Then it's the player's choice if they want to allow family members to embrace.