I was totally with you until I read your breakdown of meals & times.
Cereal for breakfast would last a couple of hours at most. For active dd probably even less.
Breakfast tends to be more substantial in our house either cereal, fruit & yoghurt plus a bananna mid morning, alternatively beans or egg on toast/bagel
I couldn't go from 1-9 without eating, my blood sugar would plummet. I always have bananas in & tend to eat around 6-7pm
I don't see anything wrong with the children having an afternoon snack of a biscuit, flapjack or fruit. It helps prevent binging I think.
If they complain they are hungry after tea they are allowed to either have cereal or toast before bed though, not chocolate or sweets.
Portion control I agree is very important & something we've lost sight of a lot but what you describe sounds very restrictive.