I agree that SCH is in a really weird place right now with lore. My first thought for them is that I don't want to see another Aetherflow ability. We already have enough of those and enough ways to spend points. With each new addition, one more thing in our toolkit becomes nonviable, because we can't do it all and something has to give (or not get used).
For SCH, I would really like to see a second dot, perhaps a gcd spell with a cooldown for burst phases. Add a buff to Ruin II for more comfortable weaving, and a proc to watch for either on dot ticks or Broil cast, that adds a potency buff to the next Broil or Ruin II cast. Nothing major, really, just something to watch for. SCH abilities have such a prepared, organized feel to them, so a little RNG would break up the monotony of broil spam.
AST--I'm reluctant giving up a quick malefic for a second nuke. The only intact redeeming features of AST in 5.x are its mobility and weaving. Every direct cast AST has is shorter than the GCD, by a larger margin than the other two healers (Glare, Holy and Broil have a full GCD cast time, and their other direct heals have less breathing room between cast and recast). Without a full rework on AST ability management, there's no room in its kit for another button, and there's especially no room in its rotation for a spell they can't weave.
AST needs a way to throw cards at enemies. It's ridiculous that the Warrior of Light can do everything we've done in the MSQ and we can't figure out how to do that (especially since we "forgot" between SB and ShB). The WoL who mains AST needs a full party of Scions to get anything done. That's.... super powerful. Yeah.
MP management is in a weird place right now. They made MP entirely a personal responsibility for healers, and outside of rezzing or excessive healing, MP is a nonissue for WHM. I am hesitant to drain mana as a dps mechanic, though, because of how much our personal damage output is already determined by the people we play with. If rez locks me out of my burst phase or using abilities, I'm gonna resent somebody.
An mp restraint on core mechanics is a penalty the healer pays for playing with inexperienced/apathetic groups.
I'd like to see that viable water spell, though, and maybe a mechanic that changes the GCD speed (a la Step and Overheated), the WHM can fire off four or five Glares at 1.5 second cast. CLERIC STANCE in any iteration. Plus all the other abilities that have disappeared throughout expansions. And some interactivity between buttons--say, casting Blood Lily during Stance or Temperance debuffs the boss with a small damage vuln up? Something like casting that viable water spell gives a potency buff to casting/refreshing Dia. I'd also love an off global ability that can damage or heal depending on target, on a shortish cooldown. A great prog tool that transforms cleanly into optimized deeps for familiar content.