Can't think of any reason to add fat unless ones goal is to alter flavor.
the only need for fat is to make a burger hold together
Fats have little if any binding qualities. Fats are, however, the source of flavor. Chemically remove fat from meat and no one can identify its source.
Proteins bind things together. Do some surgery sometime on a fat critter and see how much success one has when attempting to suture layers of fat.
Have never had issues with burger (venison, elk, caribou, moose, pronghorn, or bear) falling apart. We grill everything turning only once.