I think if I needed to cut costs and raising my fee wasn't an option, I would go this route. I have had children in the past who had their food sent due to allergies and it was fine. I never ran into the "I want what johnny has" problem and even if I did, so what? They eventually need to learn that we don't always get what our friend has anyways so it would just be teaching them young! lol
I don't mind providing the meals and snacks as I've been told it was part of the reason they chose me (there are a few dc's in my city that apparently don't supply it) but there are definitely times that I can see why it would be a benefit if the children brought their own food.