I have a vaguely related personal anecdote on this topic: back when I was a school kid I experimented with vegetarianism for ethical reasons. I quickly realised it made no difference so long as I was still at school because my parent bought the same food and cooked the same quantities of meat. All that happened was my Dad got an extra helping of steak or whatever.

Ultimately kids might have some control over what they eat at school (depending on school dinners etc), but you're absolutely right that they have little control over what they eat at home. (or rather they'll be given the option to eat what the family eats or cook their own dinners - which no normal teenager is ever going to do week in and week out if there is already an easier option going)

I do also completely agree with you about leading by example with regards to exercise etc.