Oh don't get me wrong, I've thought about it (like having an X% of remaining HP cost on Delirium), or even compromising with effects like a "incoming healing is negated up to X% health" debuff.
(I really wanted this to be the flavor of TBN in particular, to sell this idea that the DRK cannot normally toss out barrier effects and is shielding you at the cost of his own health, which would also create further incentive to use Spikes unless offtanking.)
Trouble is, whether it's for damage or defense, this leaves you in a really awkward position as either the main tank (especially on Savage raids where autoattacks hit as hard as a tankbuster in Normal, or during W2W pulls where you're already melting) or when tasked with splitting damage with the other tank -- and either way continues the trend of being the hardest tank to heal, unless you have enough self-healing to counter those effects... which would then make you easily the hardest tank to kill if you chose to ignore them for survival purposes. And I don't want to create another Bloodwhetting WAR.
Literally no middle ground so long as the healing demands are relevant, you're either a ragdoll or a juggernaut, which makes it a nightmare to balance. And if the demands are irrelevant, they would exist purely for flavor, and be on the chopping block for being unnecessary.
So I just focused on the element of "The DRK already sacrifices his HP in the course of being repeatedly lashed by his enemies." Mitigation skills give bigger MP returns (yay Blood Price precedent) and Living Dead gets easier to deal with, depending on the damage you were fed by the enemy.
Not to mention that would go against the "pragmatism" of this design. Much as I enjoy the idea of risk-reward based on overcoming self-inflicted penalties (just look at Martyr), such double-edged swords should be relatively rare or outright situational so that they have minimal impact on encounter design or overall tank balance, rather than be central to the playstyle like... oh, gambling whether or not to stack mitigation on current TBN so as not to waste damage?