One of the reasons your theory cannot be fully supported was mentioned way earlier in this thread. Nocturnal Sect's shields overwriting SCH's buffs automatically makes one of their shielding abilities pointless unless the healers have perfect coordination over Teamspeak or something. For that sort of effort, why not just go to Diurnal Sect?
I very much think that we should be treating AST as a WHM or SCH Jr, and this can easily be seen in combat. I'll use Nael deus Darnus as an example.
WHM can easily heal the party to full, even if they take Lunar Dynamo by mistake (assuming that it didn't outright kill them). Would AST helping with proactive heals be helpful? Yes, because it would mean that WHM would have to heal less -- but because WHM's healing potency is already so high, you would then risk overhealing, anyway, making one of the healers waste MP. It would be more preferable that the party be shielded throughout the fight so that WHM doesn't have to spend so much MP healing in the first place.
Now, let's use A4 as a second example. There is a lot of unavoidable splash damage in that fight. Would shields be preferable? Likely, yes. But, because SCH's shields cannot work with ASTs, you won't be doubling up on shields any time soon. So let's say the AST was in Diurnal Sect with a WHM. The healing output would be amazing, but again, you'd run the risk of overhealing and wasting MP. The problem with having two WHMs in later Coils was that the damage output was very high, and eventually, one of them would run out of MP if the run wasn't going smoothly. The other would follow suit. The problem with having dual SCHs was that the reactive healing just wasn't really there. They were meant to mitigate damage, not heal through it.
If a WHM were to run out of MP during a raid, then having AST in Diurnal Sect would be great...except for the fact that if they started in Nocturnal Sect, the point is now moot. I think that it was for situations like this that AST received healing buffs. This way, your party isn't SoL when a WHM runs out of MP. If you had a SCH run out before the AST, and you were in Nocturnal Sect, you might be able to argue that their pet could help out with the healing while you shielded...but, inevitably, you would just be waiting for the SCH's health to regen. And God forbid your party take a heavy AoE. If you're in an 8-man-raid, it won't be as easy to heal through that.
That's not to say that either combo is impossible, but it is noticeably more difficult to pull off until you have said content on farm.
You could always try running with WHM in Diurnal Sect and SCH in Nocturnal Sect, but you'll find that your roles overlap far too much. AST was meant to be a more flexible answer to the WHM/WHM and SCH/SCH combo problem, and should be treated as such. It has the ability to cover the weaknesses of both classes, so why not use the ability properly?
Edit: In response to your remark on nobody refuting your numbers, I'll admit that I won't try to. I don't know all the numbers personally. Nor do I think that you really need to. You can, but looking at basic potencies and ability rules should be enough. If not, then there's always the tried-and-true method: put it to the test in and endgame raid and see how well it goes.