Do I have to control Eos?

[SDaemon]

I wouldn't say it's entirely true to put it that way.
I can be a tank that doesn't use my cool downs. It's there but not necessary to use it. It's freedom! Would I gimp the party? yes. So would a SCH that doesn't control fairies.

If you can control even embrace to heal more frequently (if left alone fairies are a little slow), you can free up yourself to do other stuff such as putting up DOT.

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.