In Dota and in League the support role correlates with the amount of gold a character needs to do their job, it doesn’t matter what job that is, you can have standard protect carry supports (for heals and shields and other buffs), you can have CC heavy playmaker supports, and you can have damage supports that act like another damage source, you don’t have that in Hots or in Overwatch (Brigitte being a slight exception since her heals work through her damaging enemies) because the gold resource doesn’t exist and they still decided to implement their holy trinity in those games, you can’t have a damage support because that would be just another carry since there’s nothing to make it fit the role of support besides the functions of healing or shielding teammates.