But it also makes them rich. Or at least rich enough to be able to go on field trips and buy sports equipment, which is what they do with bake sale money.
I want to go on record as saying that I think this is a terrible idea. Yes, I understand the imperative to stop feeding kids lots of bad food, and I could lose a few pounds myself. But this is also a great example of why conservatives criticize liberals: because liberals believe in the nanny state, i.e. the idea that those in power know what is good for you, and have the right to dictate how you should live your life.
Liberals are forgetting a key lesson of history, and that would be the political correctness of the 1980's. I survived that era, but barely; I still have bad memories of the PC police. There is an element of puritanism in both liberal and conservative viewpoints; conservatives have their versions of enforcing morality. Someone (H.L. Mencken?) once said that puritanism is the idea that someone, somewhere, is having fun, and that they must be stopped. Telling students that they cannot have bake sales is a version of that.
How about this: if a group has a bake sale, they also have to have a fundraiser that somehow promotes healthy living, like a walkathon. Or maybe the football team (although I suspect there aren't a lot of high school football teams in NYC) asks people to pledge a certain amount of money for each point they score. Or bake sales have to incorporate some educational element, like coming up with new recipes, or working with professional chefs. What about forming some kind of organization, and encouraging the students to treat it as a real corporation? There could be a group that hosts bake sales, and the other school groups outsource it to them. Or maybe limit the amount of sugar and/or fat that can be used, which would force students to be really creative with their ingredients. It's entirely possible to make really good snacks and desserts without lots of calories, but you have to focused on doing just that. That might require more work on the part of the school administration. But it would also be much more rewarding than a straight ban. And there wouldn't be risk of a backlash. Remember, these students are all future voters.