I have yet to add up all the scenes in all the movies and TV shows where the protagonist turns down food, but I believe it's the majority of scenes in which food even appears. Our heroes always turn down food, and often because it simply doesn't look good enough to them.
In fact, one way you can tell a character is a protagonist is by the way they seem to subsist on air and attitude alone.
I understand the device, I think. If our hero is too distracted or thoughtful or bothered to eat, something important must be up. Something interesting is afoot. We should pay attention to the story, because something is more important than food.
In fact, many of our heroes "Haven't touched their food," and can't be persuaded to do so. They can scale tall buildings, defeat entire armies with one broken arm and save the civilized world on an empty stomach, unless they've been force fed by a loving lackey or grandmother.
I would love to see a superhero chomping on a cookie when the call to action comes, toss back the rest of it, brush the crumbs off the spandex costume and then leap out the window.