Let’s look at support in moba, let’s say HOTS, since they borrow stuff from their own games anyway.
The support is limited by cooldown. His mana drains fast. And he doesn’t even heal that much, deals no damage at all. Most supports key thing is utility.
OW support have no mana (infinite ammo), short or no cooldowns and can actually kill people (even mercy) but also sustain entire team.
Seriously, every character in this game is just DPS. Either fat one or healing one. Tanks and healers in MOBA and MMO deal no damage, it’s not their role or duty.