Well, Gjallarhorn would be the exception. It's quality perk is that it gets way more powerful.
Ice Breakers quality perk is that it regenerates ammo.
Thorn causes dot.
Patience and time makes you invisible.
Aclyophage symbiote gives you an extra golden gun shot.
And many more that don't increase damage. These are all fun to use (not as much fun to be killed by). Damage output does not equal fun in all cases, except Gjallarhorn.
Damage does not equal quality.
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You are correct damage does not equal quality, but almost all exotics have perks that deal with being able to deal more damage. Even the majority of armor is about being able to deal more damage. I can think of very few instances where people don't wear damage boosting gear in the place of utility.
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Well, I love my Knucklehead radar. It's gotten me kills when I should have been dead. So not a damage buff there. Purifier robes, one of the most loved armors in Destiny does no damage. There's more, but I need to go.