I don’t think eating the last piece of food is such a big deal for Americans. A lot of my friends are people from other countries, and it seems like especially in Asian cultures, people just don’t want to take the last piece. A lot of times if I’m eating in a group with people, we’ll go around offering it to each other- “you take it,” “no, please, you go ahead.” It seems like it’s out of consideration for the other people you’re eating with- someone else might really want that food more than you. I think it’s nice. Usually in the end, it gets eaten somehow, even if people split it.
Other instances of not eating the last food are kind of annoying. Like when your roommate eats all your cereal except for a few bites, but they don’t replace it, because they didn’t eat all of it. Jerks.