I got my SCH to 70 recently and got to dabble with it in EX Dungeon content. Here are my initial thoughts towards some changes to the SCH kit based on what I've played and the discussion with a few fellow healers:

(1) Summoning a fairy with a pre-charged amount of Fairy Gauge. This gives SCH a little bit of spike heal potential at the beginning of the fight and also encourage thoughtful use of fairy resummon during a boss fight to quickly recharge the gauge if necessary (and would also synergize with point 2 and 3 below)
(2) Allow the fairy gauge to accumulate with Aetherflow use even if the Fairy is not summoned. This allows it to synergize with Dissipation so SCHs don't need to hold back their stacks and wait for Fairy re-summon before using their stacks.
(3) Allow Dissipation to either or all of the below:
(3a) Reset the CD on all abilities that require Aetherflow stacks
(3b) Provide a 10s buff after dissipation expires that allows reduces the cast time and MP cost of Summon and Summon II to 0
(4) Excogition feels lackluster and should either get a potency boost or charge the Fairy Gauge more than other Aetherflow abilities (say 20-30)
(5) SCH needs a small potency boost, either on the Fairy or their base kit, but not both. Either Physick and Adlo being boosted to 425 and 330 respectively or Fairy Embrace to approximately 265 potency.
(6) Inspired by PvP but I'd like to see Aetherflow reduced to 45s (perhaps adjust the MP restored value to suit the reduced CD too)

As a random FYI, since Fey Union does count as an ability it allows the fairy to get around any Infirmity-style debuffs.

Also I heard a rumor that Excogition can't crit. Does anyone know if this is true or completely baseless? If not I might try to run some tests over the week and see.