Healers and tanks tend not to have difficult dps rotations. Stances like CS are designed to make it so that your dps is a function of how well you understand the rate and timing of incoming damage. In other words, your dps becomes a useful measure of how knowledgeable you are about healing timings, rather than how skilled you are at performing a dps rotation.

Amongst its many other functions, your fairy acts as a HoT. HoTs snapshot because they're there to help clean up autos. I know that there are some healers out there who prefer games where you spam more "heal buttons" to keep your tank alive against a continuous stream of damage, but I don't believe that manually responding to autos actually adds any complexity to your decision-making (it's just an exercise in button mashing). This is why you have unmarked cleaves and AoEs to make the timings more interesting.

I think the reason why CS is oGCD and free with a shorter recast than the tank stances is because you're usually given significantly less time to prepare for the next boss action than we do. Five seconds is significantly shorter on a caster than it is on a melee job. You need a way to differentiate between the healer who manages to squeeze off that extra DoT cast and the one who doesn't, and making CS weaving overly restrictive blurs the performance difference between these two.

If I could change one thing about CS, it would be to give it more obvious visual cues to show it's activation/deactivation to help keep track of the transition. But I suppose this is less of an issue for experienced healers, who seem to have a preternatural awareness of what buffs are on every member of the party.