Let's face it, tanking is a weird concept. Somehow we mange to compel extremely powerful, and often very intelligent being, to attack us and only us. Or even stranger is when they'll still attack other players, somehow in a pattern which makes them ineffective. Kel'thuzad isn't stupid, and yet, he keeps hitting the person most able to survive his attacks, almost completely ignoring the healers.
But aren't tanks inevitable? We can't have the mobs killing our healers, can we? So we must have some differences in how aggro is managed. And flavor will demand that not all classes are as resistant to damage, so by min-maxing a tank will emerge. Making aggro based purely on distance could help, but then how does the mob know which melee to punch? Highest damage could work, but then the highest avoidance players won't be getting hit much, so there's almost no incentive to go for anything other than avoidance.
Players could use distance as a way to tank, dragging mobs away from the pack to keep them busy, so DPS are only dealing with a few at a time. To fix this, I suggest making it impractical to tank more than a few mobs at once. Not by changing aggro, but avoidance: add a cap on the number of enemy attacks which can be avoided in a given time. In other words, after you're tanking four or five enemies, the last ones are going to be getting in free hits. A dedicated tank role cannot handle all the damage.
There will still be the few tank-type players who will be oriented more towards survival rather than killing. They would act as distractions for the strongest enemy. Think of them as the guy who yells "I'll hold him off, you deal with the [less likely to instantly kill you bad thing]!" This doesn't mean that the player class, gear, or spec will be heavily into avoidance, but they will focus on using resources for avoidance. They are interchangeable with the other melee, just taking on a different role for the given situation, and could easily switch to doing more damage.
Maybe it's not time to kill tanking, but to make it more heroic and less ridiculous. Think of when you're soloing something that shouldn't be soloed. I assume you do this at least weekly, just to keep in shape. Do you just run in with all your damage cooldowns? Well maybe, but that's for trivial stuff. More likely you're saving combo points for a kidney shot, leaving some runic power in reserve for a mind freeze, that sort of thing. You're playing more of your class when you tank for yourself.