Well no, it shouldn't, I didn't do it in school for my last... 4 years and I was never fat, just a bit unfit, I walked to/from school everyday roughly 2 miles, so 4 miles of walking each day? that's plenty to keep healthy, particularly if that's on a daily basis, obviously not gonna be running marathons, but keeps the man bra away.
More recently, due to the holidays, I've taken to offroad mountain biking and have a daily routine going with that, so you know, half an hour to an hour each day (depending on how many laps I want to do) of intense exercise, that gets you pretty damn fit pretty damn fast, and doesn't take up much time. Oh and a few weights and sit ups.
I'm no health freak, it's just strangely addictive and hey, I'm sitting around all day, gotta keep a balance right?
So I guess what all that was trying to say was, it doesn't need to be inforced on students, if they care, they'll do something about it, and if they're too ignorant to listen to anyone about the dangers of being wider than they are tall, their fault. Not hard to get some kind of routine going.