Astrologian impossible to balance as it is

[AzureFlare]

Though I really like your analysis and share the sentiment that Nocturnal has no place as it stands right now, the answer to your own question took a really sharp turn for as broad as the answer is.

Let's run back to 2.X scholar for a bit. No Emergency Tactics, no Indomitability (the biggest offenders for this comparison). You still had to frequently used Sacred Soil to support your AoE healing if you really needed it and a lot of your overhealing was simply preshielding with Succor because you would fall behind (there was no healing alternative besides Eos). You had the ultimate strength of Scholar also be its major downfall: mitigation, mitigation, mitigation. But you can't mitigate damage that is already dealt. Now, with 3.0, a lot of the weaknesses of SCH got dealt with and they got dealt with so well, they are even contesting WHM in certain scenarios: you can burst heal 700 potency onto the raid in about 3 seconds and you still have an answer to Medica 2 in the form of Eos should you really desire so. There are clear differences between SCH and WHM's AoE healing still: WHM can Divine Seal to boost itself, SCH can use Indom way more often than WHM can Assize (and for higher potency), WHM can juggle Medica 2 which Eos can't (and sacrifices Selene), Asylum has its quirks and so does Sacred Soil. That said, yes, a WHM will beat a SCH in the long run if they so desire, but a SCH has answers for situations where a WHM may find itself lacking.

Now the reason I'm bringing this up is that with 3.0, SCH went from 'my biggest asset is also my biggest weakness, but I got a fairy so it's k' to 'Oh my biggest weakness? Hold on, let me use these buttons and.. done. Oh the fairy? Yeah, just spamming heals while I watch Netflix.' And this is the healing aspect. Its weakness now stems more so from not being able to do what others can, and not from its own abilities/mechanics. Let's add that up with the points you made.

So what if Astrologian gets some flying moon with a face that can somehow magically heal things just like a fairy? You could consider this as a "solution". The whole issue about Nocturnal Sect being unable to compete with a Scholar in the mitigation department still stands.
Then what if the deployable aspected benefic and/or 15% disable are there as well? When this happens, you'll get a Scholar with White Mage raw healing capabilities. Imagine a Scholar with Cure II, Medica, and Divine Seal while having some unique abilities of their own. Astrologian in Nocturnal Sect would simply become a Scholar without it's weakness in GCD efficiency in healing.

What if, for a moment, we just send SCH back to its 2.X self ability-wise and only keep Deployment, Dissipation and Broil? Your biggest asset is mitigation and you're no longer able to 'lolIndom' when you slacked off. Yes, SCH will still have the fairy which Noct Sect has no answer to, but Noct Sect will have that 'Cure 2' and 'Divine Seal' and 'Medica' which SCH won't. The only problems that may arise is when a SCH's mitigation is needed to tip the scales when, let's say, an PLD/WAR/AST/WHM/SMN/MNK/MCH/something can't, and frankly, I'd rather blame SE for designing their fights poorly than Nocturnal for not being able to perform that obscene amount of mitigation on-demand.

If a 15% disable and maybe deployable aspected benefic would be a thing, why wouldn't this also be available for Diurnal Sect? It wouldn't make much sense that one sect gains benefits on some spells and/or abilities, rather than a variation. For example: 15% disable in nocturnal sect, 10% disable in diurnal sect. Why would this be a thing? Just simply to make Nocturnal more viable?

And why not? It wouldn't be the first time things are balanced differently for the sake of balance. If we need to do things shaky to toss someone in need a bone, then do things shaky. Clearly, there has been no time for a well-thought way to fix things and it can't be done quick. Might as well do it dirty if doing it dirty allows it to be done quick. Yes, CU was a disaster, but it was a disaster in more than a single way. Channeled Asylum/Sacred Soil was really lackluster no matter which way you bent it, and that hasn't even a thing to do with the sects themselves.

Basically, the whole remainder of the post is 'What if we did this, but oh then we overshadow SCH. What if we did that, oh SCH/WHM already has it.' Really, SCH/WHM aren't all that different from each other anymore either, they can do very similar things but in different amounts/frequencies which sets them apart. With a disparity this huge between N.AST and SCH, there are plenty of ways to give it small buffs that would still let 'the mighty SCH overlord' sit high on its throne, and even if we did overtake it: So what? Likewise, so what if we need something very similar to WHM or SCH, change a few things around and presto, AST ability/buff? And the best part, we can do this without nerfing SCH!

Yes, SE designed themselves in a corner with the sects. Yes, there are people having a huge issue with the sects and what they stand for. Yes, it is impossible to sate everyone. Yes, it is impossible to balance AST just like it is impossible to balance SCH/WHM to WHM/SCH (hello videogames people). No, it is not flat-out impossible to cut the huge difference that is N.AST and SCH, but you might not like the way it is done. We're already this deep, might as well toss N.AST something so it can compete while we wait for a proper overhaul. Just a sign from SE that says 'we haven't forgotten about you and we understand your issues!'.