One thing about the health problem is I think we have to attack it on many fronts. Supply side, demand side, incentives, etc.. I think your bmi idea would be hard to implement(for example for all these I think we need more doctors or Nurse Physicians and co, so we can spend real time with each person)... but I think you are onto something with working on the `carrot` ;) side of the equation, instead of the stick we usually use. Like taxes on cigarettes.
One possiblity is food stamps. A great number of children their families buy groceries on food stamps. Imagine with those you could only buy non-sugar cereal, milk, carrots, apples, `healthy fats`, lettuce etc..
I wouldn’t go into micromanaging food even if we’re talking about a govt program like food stamps for several reasons.
First of all it could lead to the govt micromanaging food for everyone.
Also, there are so many diets, so much conflicting research on nutrition. What works for a high carb diet won’t won’t for someone on a low carb diet or assuming high calorie is bad when someone who tries to lose weight by exercising a lot.