In a teshuva I received from Rav Elyashiv zt”l he writes that if one forgot to light on Yom Tov there is no knas. He explained that since on Yom Tov you can light all night, forgetting to light is a milsa dlo shchicha vlo gozru boh Rabbonon.
The minhag to light for each child may not have anything to do with a knas for missing. It may be based on the Gemora in Bameh Madlikin “Horogil bner havyeh lei bonim talmidei chachomim”.