I don't think it's that bad. I went my whole childhood living off of lollies until I turned about 12 and I'm not retarded. Though, I do have to say the desire for lollies did have a deterrent on my schooling, as it was all I could think about. Infact, lollies bribed me into reading and going to school which prevented me from being retarded.
When you're child is having a tantrum in a public area I'm sure you're going to realise at that point how much of a god send a dried apple or a small bag of lollies are at silencing them.
From what I believe, and it makes sense. Having a lack of snacks at home and feeding your child small portions for breakfast lunch and dinner is the way to go. Sure if they're very active kids maybe give them a bigger bowl of breakfast (without sugar and add 2 teaspoons as sugary breakfast cereals are the worst thing to give your children).
This works to train your children to eat smaller portions and feel full on smaller portions and not want to consume more and also believe that more food is better than less. You can see a noticeable difference in weight compared to the general population in my unless family compared to every single other one of my uncle's and my own family. When visiting they still serve small portions and it always fills you up.