This doesn't really make sense to me, if we are talking about mitigation they all are going to revolve around taking damage. As you've stated Warrior has raw intuition which works as a mitigation (different from the other two) and warrior has other eHP buffs like thrill of battle (which is a nice pinch heal as well). Parry only works against physical attacks, the analog on dark is dark mind which only works on magical attacks, and paladin has bulwark which works on everything but is RNG and on a rediculous timer. Self sustain wise you have equilibrium, though it does come with tank stance penalty, pld has clemecy (spammable but an even larger dps loss), and dark knight has soul eater (grit locked because reasons) and abyssal if there are enough adds to justify the huge mp cost.
This is partially true, the warrior healing bonus is not affected by things like tetra or essential or any other instant cast ability outside of regens. However, the sch fairy healing is buffed by warrior tank stance. I did some testing last night, my dark and paladin get healed for approximately 3100 per embrace, switching to warrior and the embraces went to approximately 3700, which is a 20% bonus. Similar results obtained with whispering dawn, but not with Fey Union.
Is this to say that the warrior have 20k hp in tank stance, or the warrior is at 20k before tank stance and then switches into tank stance to get 25k, but remains at 20k because they don't get healed for the switch? If its the latter (and I think it is) then either 1 of 2 things failed:
(1) the warrior entered tank stance too late to be healed by the healer and did not have equilibrium up to heal themselves (in this case the pld and dark may die as well since the server tick may not see the mitigation until after the attack if it was put up this late)
(2) the healer does not understand how warrior tank stance works (nothing you can do about that, it is alarming considering how long warrior has been around. More frightening I've met warrior's who didn't understand they did not have mitigation on their tank stance).
The real advantage of warrior's tank stance is the fact that they can very fluidly switch stances at no cost to themselves other than the damage penalty from tank stance. Warrior's do have the highest damage penalty in this respect, but when you consider how little you need to be in tank stance in most single target fights the lost gcd from dark knight or paladin activating tank stance for such a short period of time likely balances warrior's higher penalty (I wonder if anyone has mathed this one out).
This is also ignoring the fact that in most of savage, even undergeared tanks are able to leave tank stance for 99% of the fight (I have not cleared v4s but we are progressing and I see nothing to indicate I must be in tank stance yet). When you take that into account the short cooldowns of warrior put them into a mitigation tier of their own in comparison to dark knight and paladin.