Why not? Asking your healers to spend more time watching EM and the CT raid windows is a bad thing.

why? I personally find it easier to prioritize healing targest with CTRA. Being able to put all the tanks or rogues or whatever in one "group," or being able to position the groups I'm responsible for together.

There's still PoH.

And you said yourself, "the groups I'm responsible for" -- clearly you need group assignments to make sure that through a lack of communication you don't end up with one warrior that has no one in range to heal him because everyone assumed someone else had it covered. And as groups shift and move and change assignments over the course of a run, I think that'd get confusing to maintain. It's far easier to just have the default assumption of "you heal your group."

And really, there's no cost at all to not giving mages/locks tranquil most of the time. They rarely need it. On the fights where they truly do, I rearrange groups so that they get it, of course.