It's a mix of the whole package together and yeah that's another huge part of it.
Proper AF stack usage *max dps while having them when heals are needed*
Learning to trust your co healer and directly healing only when stuff from your kit needed or damage is too high on the whole party/split high dps on party memembers
Managing your fairy as the main healers co healer while you dps otherwise
This is pretty different from how most people view a healer, so while I understand why people feel sch is weak the class isn't and is very strong when all your management of it's tools are down.
If people want a more direct healing job and like the concept of shields I'll always point them in the direction of AST and there is nothing wrong with that to me.
This really just reads like a list of assumptions about how other healers collaborate that isn't super accurate, though. Mainhealer/offhealer has been kind of a dead concept for years (and I hope this is the tier somebody convinces FFLogs to start ranking healer pairings for combined DPS), something that's only more true now with Clerics dead in the dirt behind us and there's nothing prohibiting shifting the burden back and forth every GCD if needed. Especially since, in the current structure, WHM has highest potency per GCD and so if somebody's blowing what could be a DPS GCD on a heal, it should be the AST or the SCH first with WHM the one that only gets tapped in when necessary.
Like, the fairy adds a micro component the other healers don't have, but it's not Coil anymore and the actual allocation of healing GCDs is a lot more involved now than the old default "I am here to DPS, the fairy is the healer!" mindset.