Besides getting them to stay together, what other reason would there be for adding breadcrumbs to meatballs. Do they impart any particular flavor or texture?
In meatballs or meat loaf or even burgers, breadcrumbs are sometimes added with egg.
The bread, if unseasoned, doesn't change the flavor much except to dilute it.
The texture is definitely different. It is smoother and spongier. The breadcrumbs also soak up liquid so the product doesn't lose as much and stays moister.
Purists often decry the use of breadcrumbs in things like burger patties. For myself- I will add breadcrumbs when I am in the mood for the breadier texture- often when I will be adding extra liquid flavorings like Worcestershire or liquid smoke and want to strengthen the structure a bit.
The motivation is mostly textural. The major motivation for using bread crumbs is if they are soaked in milk, making what is called a "panade". Since meatballs and meatloaf are often cooked to well-done, they tend to be tough and dense. The panade does act as a binding agent, but, more importantly, the milk activates the starch in the bread to form a gel. This gel acts much like a fat, lubricating the meat's protein fibers and discouraging them from forming a tough matrix. Enzymes in the milk can also help tenderize tough cuts of meat, however, that would likely take longer than the average meatball recipe allows. Finally, if the meatballs are fried, breadcrumbs can help crisp the outside of the balls (especially if the balls are rolled in breadcrumbs on the outside).
Meat stretcher. The crumbs from sliced bread, leftover porridge, broken bits of crackers or chips can be put to use to stretch the recipe yield.
Bread crumbs do not help meatloaf hold together. It was started back in the depression when they wanted meat to stretch out, they would add the crumbs. The thing that hold meatloaf together is the eggs.
Bread with milk or water will suffice. Bread is the important additive as it has rising agents and this mixed with ground meat serves to lighten the texture and slows the hardening of mincemeat once cooked. It's not used to extend the meat yield.