Let's go by release order.
WHM currently has 10 buttons dedicated to GCD healing (11 if you count Misery) and 5 buttons dedicated to interacting with the GCD.
The full list is:
Cure, Cure II, Cure III, Medica, Medica II, Afflatus Solace, Afflatus Rapture, Regen, Esuna, Raise, Pressence of Mind, Thin Air, Plenary Indulgence, Temperance & Swiftcast.
That's between 15 or 16 Abilities which is literally half our toolkit and from the abilities I mentioned in optimized play you'd prefer to only use 3 of them, maybe 4 if you see Temperance more as a mitigation rather than GCD boost. Even in unoptimized play you'd probably use maybe 7 or 8. And you know what? If Misery wasn't a DPS loss those 4 unoptimized play buttons would be optimized. Crazy right?

SCH currently has 5 buttons dedicated to GCD healing (I don't count summoning the fairy even though those are GCD buttons) and 6 buttons dedicated to interacting with the GCD.
The full list is:
Physick, Resurrection, Adloquim, Succor, Esuna, Fey Illumination, Deployment Tactics, Emergency Tactics, Dissipation, Recitation and Swiftcast.
That is 11 buttons dedicated to something that's most optimally used during downtime or else it's a DPS loss. Not as bad as White Mage but that's still a third of the toolkit dedicated to something that isn't really used in optimized play and if used it's for different reasons, like Dissipation being a tiny DPS boost. But the more damning issue is that SCH is a barrier healer that's being punished for barrier healing.

AST currently has 8 buttons dedicated to GCD healing and 6 buttons dedicated to interacting with the GCD.
The full list is: Benefic, Benefic II, Aspected Benefic, Helios, Aspected Helios, Ascend, Macrocosmos, Esuna, Lightspeed, Synastry, Astrodyne, Horoscope, Neutral Sect & Swiftcast.
Similarly to WHM that's nearly half of AST's kit which wouldn't be as jarring if AST didn't need so much space dedicated to it's card mechanics. But unlike WHM there is no Lily mechanic trying to return 75% of DPS for GCD healing, in fact AST might have the most OP oGCD heals of them all. Synastry felt out of place in AST's toolkit forever and while Horoscope can still be used without a Helios cast, Neutral Sect does not. It can't even be used for mitigation only, you have to GCD heal with it.

SGE currently has 5 buttons dedicated to GCD healing and 4 buttons dedicated to interacting with the GCD, 5 if we include Toxicon.
The full list is: Dosis, Prognosis, Egeiro, Pneuma, Esuna, Eukrasia, Zoe, Pepsis & Swiftcast.
That's 9 or 10 Buttons and similarly to SCH a third of out toolkit of which we don't really use much during the fight.
(2/3)