I cannot imagine being even a remotely good healer by leaving my fairy to auto-heal whoever she pleases, her AI simply isn't that good. Maybe it was okay back when we couldn't control her while casting, but now there's no excuse. It gives you far more flexibility on who should be healed, as well as allowing you to precast heals.

On a boss like Caduceus, yes, I want her to be healing the tank even when they're at full health as it allows me to heal them that much sooner after they take damage. If I waited for her to decide when to start healing, the tank is likely to suffer another hit before she's done, which is something you don't want when fighting a boss that's capable of dealing 50-70% of the tank's health in damage in less than a second.