Then this mightiest of gods actually allowed lesser gods to wield this power. This actually fits really well with the role of the Unconquered Sun as some good, virtuous person.
"I am Sol, a powerful warlord who just used semi-divine mortals to overthrew my boss so I can rule over Heaven."
"I will now give my subordinates the ability to create semi-divine mortals who can overthrow their boss so they can rule over Heaven."
"This is an intelligent course of action."
Games of Divinity has Sol being
very pleased that the Solars couldn't multiply or breed, lest they build Celestial dynasties that could one day threaten his dominion. He might even have deliberately restricted that capability, I don't recall. Him handing out the ability to create Exalted is totally out of character. If nothing else, it's about as responsible as the US winning the Cold War and then deciding to hand out its spare nukes as party favours at the UN.
Moreover, even if passing out weapons of mass destruction to bureaucrats was evidence of being a good, virtuous person, I don't agree that being such a person should be Sol's role. He's a war god, conquering king, and fiery defender of Creation. He has no more need to be an objectively great guy, Superman cast in gold, than Jupiter, Ra, or Indra. The latter is particularly relevant, given he's sometimes depicted as using thunder to interrupt meditating monks, lest they achieve enlightenment and become more powerful than him.
Plus, you can put all sort of power politics into it if you want to be more nefarious. From "leave me alone to my games, here's a tool for that" over "I did it to undermine the other Incarnae" and a whole bunch of other things, all that fits with Ignis Divine granting other gods access to the Exigence.
Honestly, it's such a daft decision that I'd rather play it straight as
being daft, and just have Sol be tricked out of the secret of Exaltation by someone. A lesser god, or whatever. It'd be far more mythological, it'd make it clear that
he's not perfect - far more important than making it clear that Solars aren't, given we can play the latter - while acknowledging that it's a stupid thing to do.
So what do we actually get out of Exigents? Both for the setting and individual stories.
As just mentioned, they're simultaneously tied to Solars and sidestep them. They are also a type of hero that's new to the Age of Sorrows, so it's a counter to "everything revolves around Solars" and "Solars are the only heroes that can save us".
I can only disagree with the medicine being proscribed here.
I agree that there was a serious issue in the presentation of Exalted by the time of second edition, in which the Exalted - and within their ranks, the Solars - were regarded as the only threats or actors worth taking seriously. Aside from the Incarnae and Yozis, everyone else was essentially a beanbag, and the fanbase reacted with incredulity whenever it was suggested that a non-Exalt might have got one over an Exalt, even briefly - much less defeated or exceeded them. Similarly, it was a bit suspicious if a "Solaroid" was overcome by a mere Lunar or Sidereal, much less one of the Dragon-blooded!
This was a cocktail of four elements:
a) hype without balance, whereby the deliberately flowery, hyperbolic, or just plain pump-you-up references to Exalted/Solar power and importance within the setting began to eclipse the reality checks and other elements meant to counter it or give it context. This wasn't helped by the echo chamber of forum discussion, occasionally fed new tidbits like "mortals don't get to win".
b) poorly-directed focus, whereby more and more space was dedicated to the specific capabilities of Exalts, instead of the world within which they operate. Similarly, exploration of the minutiae of Exalted functions and genesis, rather than dismissing it as rightly irrelevant. This also wasn't helped by the last few years of the line being dominated by little but reams upon reams of steadily more specific Charms for Exalts.
c) a broken system, whereby only those with Exalted tools could survive for any meaningful length of time, and Exalted tools had to be exclusive to Exalts, and Solars had by definition the best Exalted tools of the lot.
c) writer favouritism and lack of exploration, which led to dumb shit like the Bull of the North being central to every other plot point, even thousands of miles out of his way, or entire plots hinging on the fact that only a Solar would be allowed to pilot a given super-artifact, or gods automatically loving Solars and hating Dragon-blooded.
The solution is to dial back on the excesses and refocus the game, presenting old ideas in fresh ways and spicing it up with new ones. Introducing a new set of Exalted is not, in itself, a solution. Especially not when they occupy already-extant conceptual space, and are intended to fill any and every role by being everything and nothing. That's just doubling-down on the problem, because now the setting tells you that the Volcano God doesn't have magmakin servants and a soulsteel champion forged from the sacrifices thrown into the molten heart of his home - he has a Chosen of the Volcano God, because only the Exalted are important. The scion of a City Father, seizing power from their parent by dominating the dark and unseen side of the streets as a crime lord, is not on the table, because she should be a Chosen of the City Father.
If the problem is too many labels, you do not solve the problem by creating an impossibly broad new label to paste over a bunch of the old ones.
Similarly, to go back a little way...
Well, imagine this:
When the gods sought to overthrow the Primordials, they used the mightiest tool of all times - one that allowed them to channel their very being into mortals, the only way they had to bypass the geas laid upon them. This tool was the Exigence, and after the war it remained in the custody of the Unconquered Sun.
You can have the Exigence as the greatest creation of Autochthon. It's easily the perfect tool because it's capable of shaping essence like nothing else, it can instill creativity and life and all those other things. It's even a perfect contrast to his sickness and fits very well with his theme of surpassing his limitations.
Or you can leave that out, the origin doesn't matter as much after all. Maybe Ignis Divine created it on his own, maybe the other Incarnae helped, maybe it was even a collaborative effort by all the gods or came from somewhere else entirely.
For this entire section you could replace the word "Exaltation" with "Exigence". It's just another layer of complication in a part of the setting that's already too explored. You don't need to create something new to return mystery to the setting, especially not when that "new" thing is just a rehash of an existing element.
It's already been hinted at that getting an Exigence can be as much a matter of celestial politics as anything else. Getting celestial politics more involved in creations story is a good thing in my book, as long as it's not overdone and turns celestial politics into all that matters. Well, the Exigents actually accomplish that.
It's a challenge to players independent from Dragonbloods - which are too tied to their faction - Lunars (same in some ways) and Sidereals (which don't rule territory in Creation). At the same time, they're more human than gods are and can tell different stories.
It actually allows small gods to have an impact on the setting beyond just getting curbed by every major thread. The story of Janest is a great example of that.
Again - if the issue is that gods seem irrelevant in the face of the Exalted, the solution shouldn't be to
give the gods Exalted. That's just escalating further. It's like responding to a guns problem by making gun ownership mandatory instead of implementing gun control. The ideas that go into Exigents, like the Strawmaiden, are made
less interesting and useful by the addition of the Exalted label.
It makes the setting
more homogeneous, not less.
Your ideas for what makes an "Exigent story" unique are solid, but ultimately I find Exigents more of an obstacle to fixing the problems facing Exalted at the end of 2e than an actual solution. Hell, they'd even be more interesting as an umbrella term (like behemoth) for pseudo-Exalted, attempts by non-Incarnae to approximate their own Chosen by various manifold means, rather than an actual distinct category of real Exalted with... basically no uniting features.