Do I have to control Eos?

[chococo]

There is a difference however. Not controlling Eos is a healing loss yes, but short of SCoB a SCH by themselves with little involvement from Eos is enough to heal an encounter readily and ably.

I'm not disagree with what you said there. But put it in another perspective, if fairy can heal more to reduce sch's healing input, sch can do more dmg (benefiting the group). It's just the difference between a top notch player and a good player.