Or, try running any job while afking for 2 out of every 3 GCDs. Same difference, in most cases.
It's not a "Healers must dps!" thing. It's a "Make use of your time, so you're not wasting ours" thing. And it's expected of every job. It's just more obvious when someone is doing literally nothing, or constantly overhealing, than performing their rotation poorly.
So long as we're expecting all tanks to play basically identically, though -- quick to point out any functional imbalance -- and the devs continue to have difficulty balancing in different styles, rather than from small changes on a shared template, that's going to be tall order. I think both the community and the devs are going to have to bend a bit before we can really see a satisfying tank roster.
If the problem is that consistent, though, isn't the issue equally likely to be simply that... tanks and healers aren't attractive enough? I mean, it's one of the two: the designs are somehow perfect, but players, being foolish creatures, don't like them, or the designs aren't well suited to player desires. Which sounds more likely?
DPS toolkits can afford to be self-involved, to have their pace ebb and flow through their own mechanics. They don't have to be immediately reactive/preemptive to outside conditions. That allows them far more depth. But there's relatively little of this among tanks, especially for Warrior as of the Inner Release simplification.
And as for table-top RPGs, just consider any of the DnD style video games you've approached, or any system with ranged or first-strike mechanics; they, not a tank or healer, are the bread and butter of combat. Many enemies can be defeated by sheer range and power, or through ambush, rather than spending time unnecessarily on purposely accepting damage (even if mitigated) and replacing the lost HP.
And then there's the responsibilities. Perhaps if the responsibilities of DPS were equally visible, a bit more of the ostensible tank/healer burden taken up by DPS, then the other roles would be more attractive, at least relatively.