I do not think they should have their childhood disrupted by media interest.
They do not have their childhood overly disrupted on a daily basis. Admittedly they have to turn out for royal events which are a right pain sometimes, but George actually enjoys going to watch football with his dad, and Charlotte tennis with their parents in their working rôles.
Do you know the families? How is our curiosity satisfied at the expense of their childhood? I have a colleague at a school royal children attend, and you wouldn't know who the children were. There is no media interest allowed, visitors are respectful, and it's daily school business as normal, (with a bit of added security involved).
Their childhood is far less disrupted than that of many other children's. Even when the royal children are exposed by the parents, like in the videos of Catherine's recovery, I think it's fine to show the whole family together showing their support.