From experience, the moment that you make a defensive action cost dps to use, it stops being used outside of progression. I think at that point you're better off just removing it altogether.
I agree with Snow's point about tank healing being too passive, but I do think there are other approaches. A really easy way of doing this is having a healing effect scale on the amount of damage taken recently, or based off of how low your HP is (i.e. a Minus Strike type effect). This way, you have negligible healing under normal circumstances, unless you've specifically timed the move against a big damage strike. And I think that timing should always be central to tank defensives, and giving tanks lots of reactive healing solutions to compensate for a lack of anticipation doesn't really fit the role.
Another approach is to have defensive cooldowns have offensive value. In Heavensward, Raw Intuition and Vengeance both generated Wrath stacks, so you wanted to use them under Berserk in order to land more Fell Cleaves. It discourages players from sitting on stockpiles of defensive actions to otherwise be pressed on demand, and encourages you to swap in a way that takes advantage of your increased tankiness during burst. It probably fits more with a Warrior aesthetic, in line with damage resistance during D&D barbarian rages.