I fail to see how it really adds stress. You, as the tank, shouldn't be relied on for cures, but it should be an augmenting force to your tanking skills and the survival of your party.
We know the movesets of just about everything we fight these days, and in all tanks should know their limits on taking damage. If I'm in critical health, I'm not going to be curing someone else because the next move Ifrit does could probably kill me. But if I'm sitting at high yellow or white HP, where there is no risk of any of his moves from his entire moveset killing me, then I'm free to throw out cures or buffs depending on the situation.
Honestly, it's literally no different from curing yourself, except for hitting a function key to target someone else. You wouldn't say being responsible for your own HP is too stressful, so how would adding one keystroke add so much stress that it would be undesirable for restoring an allies HP (in addition to your own, in addition to enmity)?
EDIT: You say that it's a distraction because you should be focusing on your own survival.
This is false. Tanking it about the survival of your entire group. It doesn't matter how well you stay alive on your own. If the rest of your team is dead for any given reason, then you've failed and you likely aren't going to finish the fight you're in.