Embrace + Physick add to similar potency than a Cure + Regen or a Benefic + Aspected Benefic. It doesn't match the healing output of Cure II or Benefic II, unless you Rouse it or unless you're considering the tooltip potency to add both spells to 700 potency when your fairy healing output is not that of an actual 300 potency heal. If you're seriously claiming that using your fairy to add something that's very similar to healing over time effect + basic heal is equivalent to a stronger built-in GCD heal, it means you're underestimating the value of having a GCD built in second tier heal (Cure II/Benefic II). Your ET + Adlo + Embrace adds up to what exactly? An output that matches an 800 heal (not 900, because we're talking about healing done not adding up potencies from the tooltip) every 30s (unless it crits, but RNG), which both WHM and Diurnal AST have available all the time without even needing a cooldown. That's the point.
You point out Indomitability, but you forget to say that it uses a stack, which lowers the amount of Lustrates you can use. Some people were claiming here that SCH was better because they can spam Lustrates. They can, but then they lose a 400 potency AoE heal. I have absolutely no idea why you're denying that, since stack management is the core of the job you play - and the most fun aspect of it in my opinion. And then again: WHMs can reach more than what you reach with Indomitability by using Cure III, as it was pointed out in here.
My discussion was never around being able to reach the potency or not, but around the fact that, to reach those potencies, your good and skilled SCH had to burn three cooldowns (you mentioned three of them yourself) while a WHM can do it with their GCD alone and by using less GCDs. Potency is not what makes a main healer better at the job, it's the ability to react to situations no matter what decisions you have done before - if you burned ANY of those cooldowns shortly before, for any reason, you won't be able to react to a situation as easily as a WHM can. To be able to even out (or even pass) what a WHM can do, a SCH has to know the fight (you said so yourself about precasting), which you don't when content is launched. A good example of this is the difference between Asylum and Collective Unconscious in healing. Asylum heals for less than Collective Unconscious, but the logs point out that its healing output is higher. That happens because WHM's can burn Asylum more freely than ASTs can do it with CU since Asylum is a pure healing skill that is not tied to anything else. CU has to be saved to add mitigation and healing after big bursts. The fact that a WHM can have Cure III available at all times to heal big burst situations is what allows them to use Asylum the way they do. The same can be applied to SCH: if you have to burn an extra stack for any reason, it may throw off your entire rotation. This is a setback. Does learning the fight help you with it? Of course, but it doesn't make SCH a better healer in all contexts.
The OP asked about the best healer, and I argued from start that this discussion requires context. People were arguing that SCHs were being added to end game progressions groups because of their healing skills. That is false. If you want security in healing, you're adding a WHM to the party, because they have the best reacting toolkit in the game. Are you going to deny that when you just stated yourself that you need to precast things, have Eos available (which reduces the overall DPS/Utility Selene brings), and have at least one stack available to match (or pass by a small margin) what WHMs do with their GCD alone? If you can't see that having to make a list of choices and priorities is a core component of SCH's basic healing toolkit, then there's no point in discussing anything with you.
I never ignored Emergency Tactics. I brought the cooldown up several times. You were inflating what it does, as you are with the fairy healing output. You claim that ET does not prevent a SCH from using any other spells, like I claimed. I may have not made my point clear. What I mean is, once you use ET to burst heal with either Succor or Adlo, you can't do it again until it's out of cooldown. It means that, if you find yourself in any emergency situation that required you to use it to heal unexpected damage, you may not have it to use it when you were planning to. The same is true for stacks.
Want an example? A1S, if any missiles hit the floor; it's rare nowadays, but it may happen. WHM/AST can spam heals and then deal with MP management in different ways. SCH's may not be able to do that if they have used ET/Stacks before. What I'm pointing out is: WHM and ASTs don't need cooldowns to do that, SCHs do. Spamming Succor doesn't help, because once the shielding is applied the spell is worth only 150 potency, and if that shield fades away before the next AoE damage comes, it's wasted.
If you want to mention all cooldowns available to WHM/AST, then let's do it. You're not going to like the result. In another thread, people started arguing about MP Management (WHM versus AST). WHM was beating AST by a margin of 3K extra MP, but in the calculation they ignored a few tricks AST can do. When those things were pointed out, the table flipped and WHM started losing by way more than 3K MP. Since the majority of the SCH's cooldowns you mentioned and the smart combinations you pointed out are used to match the natural potency of WHM, adding Assize, Tetra, Benediction, Divine Seal, Presence of Mind and Asylum will flip the table in an unpleasant way for SCHs when placed in reactive contexts (which is the actual context of a fight).
And finally, about WHM being restricted by MP: all healers are. SCHs can be drained out of MP easily if they don't know the fight and have to do extra precasting of their shielding spells because they don't know when damage is coming. The only reason SCHs don't struggle more with MP/stack management while learning an 8-people raid is because they're usually paired with a WHM that takes the healing burden away from the off-healer with their (I'll say it again) very good reactive toolkit - which is not matched even by AST. Also, WHM's also have means to refresh MP; you make it seems like WHM (or even AST) struggles with a 11-12 K MP pool (which is what we had when Savage was launched), when in fact we were finishing fights or pulls with more than 7K to spare.
Being "equal" or "slightly better" in main healing when fights are well learned is meaningless. This is the actual point that someone started when they said that SCHs need to get out of their high horses or something like that. SCH is being overestimated and its healing output is being inflated by the SCH mains that are posting here, which is sad because the job does not require any of that since it's amazing no matter what. The point I have been trying to make is:
WHM: is the best reactive healer, with the strongest toolkit built into the GCD. It's the safest healer, with no strings attached to skills that prevent them from doing high potency healing. DPS output can be high, but it's all related to accuracy.
AST: has a very decent toolkit built into the GCD. It's not the safest healer, but it can support the party in several ways while keeping its healing capabilities. It doesn't have a very strong DPS toolkit, but its DoTs are very strong and bypass accuracy checks.
SCH: is the strongest healer in DPS output. It has a wide number of healing tools, but they're tied to a master mechanic that requires management and their more advanced healing spells require precasting to be effective. Their party utility and support toolkit is not available all the time, because it depends on the fairy they're using.
They're all good, they're all amazing in what they do, they all get the job done in all contexts, they're not necessary in any way to clear any content, and they're not better than each other in all aspects. You're going to miss something no matter what you choose. The reason why the WHM/SCH combo was being favored is because it's the most balanced; you get the best main healer and the best off-healer when you don't know the context of the fights. The problem that I see now is that fights were not designed to favor other combinations or even to allow progression with any combination (like SCH main healing and AST off-healing). That can change if they design fights that add more value to AST's toolkit; then we're going to see which of the other two is going to be dropped. My bet is that SCH will keep its spot, because of its off-healing strength. But again, that doesn't make them the best healer.