18s of getting only the aegis part of PoH = 8*0.7*base = 5.6*base. So the benefit is 0.25*5.6*base
4 full casts of PoH = 4*1.7 = 6.8*base. So the benefit is 0.25*6.8*base
Your rationale is that this is why its better to use it like that. However you have forgoten that you are using AA 1.5 times more if you do so on Cd. So the total benefit of AA on CD is 0.25*5.6*1.5*base = 0.25*8.4*base, which is ~24% larger.
I am just comparing a small delay where all you get is aegis to effectivelly full use of PoH over a short window. This is of course not realistic, because you do have overheal and loss of aegis no matter what and you also have spirit shell to contend with, which might cause you to lose all the aegis you have stacked in some cases. Also you don't really just spam PoH. Other spells that you might cast like PWS or PoM also benefit from it. Overall the increased uses almost always outweighs the benefit of more efficient usage.
AA is 18s duration with a 30s cooldown. You will at most be without AA for 12s, so if you are delaying due to damage that is coming in less than 10s or more than 30s you are gaining nothing at all by delaying it you are wasting use of a cooldown, which will still be either active or ready again when you need it.
All our highest HPS sequences involve effectively using AA on CD. It is just how it is and nothing can change it.
Intuitively it might seem that using AA strategically is better, but in fact if you model any non trivial damage it turns out that using AA close to on CD is simply better. What you are doing by trying to synch AA is mostly skipping uses for comparatively small increase in the benefit you get from AA. Effectively you are simplifying the spec by sacrificing a certain amount of healing.
The major reason why ppl don't often get better results by using AA on CD, is because it makes the playstyle very complex and the vast majority of players (including me in some encounters) just can't execute it well. For example on our hc empress tries, I just can't deal with the added complexity of the extra use of AA between spirit shells in p1, so I skip it. This definitely costs me healing though I don't delude myself and say that I am making better use of it.
As for using SS on 2 groups and then using AA to heal after that is just plain wasteful. Even if you can put spirit shell on only 3 ppl on a third group it is definately worth using AA and using the extra healing on spirit shell or you if the burst is not a single hit you can time spirit shell to overlap the damage period.
In summary a lot of people might think that not using AA on CD is making better use of it, but in any senario where the incoming damage is not trivial and almost every case when you are bubble spamming this is not true, because the CD is so short that even small delays produce large loses in healing.
This is exactly the kind of linear thinking that leads you to incorrect conclusions. How long do you think the aoe phase is going to be? Is it going to be 30s? In that case you can use it before hand AND during to boost BOTH the DA before AND the healing during the burst AND the DA after. You are just wasting healing but not gaining anything because you still get use of the CD. Remember its only really down for 12s if you use it on CD.Id rather get DA stacks on the raid before the aoe without AA, while it might take slightly longer, that just means you start it 1-2 casts earlier.
Then during the big portion of the AOE you have 25% more healing to actually do RAW healing on top of boosting whatever aegis might come out
What if you use it on cooldown, during a phase transition where NOTHING is happening. Then immediatly into the phase its a heavy AOE phase and oh look, you don't have AA up.... then your AA went 100% to waste.
Again how long is the phase transition. Is it 5s? 10s? 30s? How long is the burst phase. In many cases a long transition where nothing is happening is a perfect opportunity to use AA stack some aegis and restack evangelism quickly so you can use AA with spirit shell on the big aoe phase.
Feel free to talk about any encounter in the current tier you like and I will prove to you conclusively by modelling it that using AA on CD is in the majority of cases more healing, even AA is used during low damage periods by using it on CD.
The reason is simple in most cases delaying AA, rather than synching AA with incoming damage it ends up just dropping a use of it, because it duration is very long compared to its CD.
In 5.2 you always want to synch AA with spirit shell and that means any use of it you get in between spirit shells is a bonus and hence using it on CD is just an extra use that you can get without sacrificing anything at all.
In 5.1 in 25man since you really do want to synch AA with spirit shell most of the time you get the same result. Not using is just skiping a use, you don't get any benefit from skiping it.