DPS do have other things to their job, support and damage. However, the balance of the game is based off damage. If you remove damage from Tanks the entire engine would have to be recoded to change enmity. If you remove damage stance from healers then you risk losing all of your raiding high end population, due to the fact that most content can no longer be cleared.
So, SE would need to recode their entire game to balance it around such changes.
Honestly, Everquest did a "different" approach:
Tanks had:
Damage, Sustain, Self-Healing.
Healers Had:
Healing, Damage, Buffs, Wards
DPS Had:
Support, Damage, Debuffs, DPS Buffs, Hate Transfers.
Giving DPS classes debuffs, DPS-buffs and hate transfers would fix the issue.
Imagine Black Mage having a buff, which transfers 10% of the damage he does to the tank as enmity?
What if Ninja had a buff that increased a target's casting speed by 10% every time he scores a critical hit for 10 seconds?
What if Dragoon had a debuff which increased the chance of the entire raid to score a critical hit against the mob?
What if Machinist had a buff which increases the attack speed of the raid?
What if Bard had a buff that increased the damage of another person and gave them a proc that lowered enmity gain?
What if Bard and Machinist had a buff that raised the damage of a tank class and gave them a proc that increased enmity gain?
What if Monk had a raid wide buff which increased the ranks damage reduction?
What if DPS had to do more in the raid then just damage? In Everquest a lot of times DPS classes had to do the mechanics of the raid, like hitting levers in the right order to weaken the monster.
In the Djinn Master fight, DPS classes had to jump on keys in a correct order to make a song or the Djinn Master would not take damage and constantly pulse AOEs.