When we feed our babies, they're likely to get food all over their faces, their hands, and the surrounding area. They don't have to worry about that though, because you'll clean that up. When they're a little older, and they're eating 'grown up' food with the rest of the family, they still don't have to worry about cleaning up. You'll take the plates, the cutlery, and any food wrappers, and you'll wash or dispose of them as appropriate.
You have been disposing of your child's waste since they were born. That's programmed them to expect you to do it for them. That means sticky wrappers and other bits of trash are likely to get handed to you for you to get rid of, rather than taken to the bin. When they can walk and talk, point out the bins and tell them you expect them to use them!