Here's a tank's stance on this.

Enmity is everybody's job, but the balance is slightly skewed, say 80/20 Tank/DPS. Yes, its my job to generate and keep hate, but its your job to drop hate where you can. Ask yourself a simple question: When is having MORE enmity as a dps/healer ever a good thing? It creates an artificial cap on your overall potential. Quelling/Smoke/Elusive are raid DPS boosts, because it allows the tank to spend more time out of tank stance and allows DPS to keep going ham sandwich.

Consider it this way: You getting rid of something you don't want, gives me more of something I do want. Be nice to your tanks, they keep you from going squish.

These things said, if you're using hate reducing skills and still pulling off the tank, the tank is doing it wrong. I have more enmity generation than you do enmity reduction, and the onus is upon me to generate more than you can reduce. However, consider the investment for your hate management compared to mine.

BLM/SMN/BRD/MCH/NIN/DRG: Use a oGCD that in no way negatively effects your output. (For the DRG's complaining about Elusive, you can use it right before the boss jumps, or during phases where the boss is effectively immune. ((A9S after Faust dies but before he is melted, A10s during Spin to Win after the add is dead, A11S before limit cut.)

Investment in generating more hate as a tank:
-DRK: Grit costs 1.3k MP(75% of a dark arts), eats a GCD, reduces our damage by 20%, locks Blood weapon(less dark arts) and our enmity combo generates no MP(less dark arts).
-PLD: Eats a GCD, reduces damage by 15%, no Sword Oath double AA, and Rage of Halone is 90 potency loss over Royal Authority.
-WAR: 20% less DPS, locks Fell Cleave, but not a lot of downsides here.

Because of the DPS meta and benefits that high DPS brings(shorter fights and less mechanics), optimizing DPS output between mechanics is a major boon to clearing content, and all party members are responsible for that. There is zero DPS loss for popping quelling/smoke/elusive, there is a major DPS loss for going into tank stance and using enmity combos. Its the Tank's job to stay over DPS, but DPS have no excuse to not make it easier.