Couldn't you say the same about tanks though? Tanks also aren't DPS, so I could use the exact same logic to say "it doesn't make any sense whatsoever to let them do higher DPS than healers. If they did, I'd just play DPS instead."
Consider that dealing damage is more synergistic with a healer's goals than a tank's. A tank's goal is to endure, regardless of how long that takes. Survive until the party can win. A healer's goal is to heal and prevent damage as much as possible, and there's no better prevention of damage than the enemy being KOed, because that's a 100% damage mitigation.
"But aggro!" Except aggro doesn't need high damage to be generated because of tank stance. And even if tanking wasn't so mindlessly simple, aggro isn't inherently associated with high damage. High healing actually generates more aggro than damage generally, and that's not to say you can't have effects that generate aggro without doing damage at all. Flash says hi.