The answer to why Why Do Mortals Rule A Lot Of Places is blatantly obvious, and that is Exalts are supposed to be RARE. I know games and players take the approach that you can't go five feet without tripping over an Exalt bu even for DBs you've only got a couple of ten thousand in the world *period*, that's not even enough to fill a decently sized city, and for the celestials even if you go with the approach the hard caps are no longer in place, between the Solaroids and the other Celestials you're maybe cracking 1500. That's not a lot of people spread out across a large scope of land!
To use this as a jumping-off point, in the
Shahnameh, the national epic of Iran, the main character Rustam is easily one of the strongest men in the world. His opening act of heroism is killing an elephant with a single strike while still a young teenager and when he is a man he has slain the White Demon of Mazandaran and his entire army, tamed a horse
that kills lions, single-handedly conquered the unconquerable fortress of Nariman, slain a dragon, killed countless demons and freed the Shah himself from the grasps of evil. He is in every sense of the word, a hero beyond compare and is regarded as such. When pressed by his sovereign later in a moment of stress, grief and anger, he responds that:
Ferdowsi's Shahnameh said:
In his wrath he struck the hand
Of Tus, thou wouldst have said: "An elephant
Hath struck him!" Tus fell headlong to the ground
While Rustam passed him by with angry mien,
Went out, and mounted Rakhsh in wrath, exclaiming:
"I conquer lions and distribute crowns,
And who is Shah Kaus when I am angry,
Or Tus that he should lay a hand on me?
My might and my successes are from God,
Not from the Shah or host. Earth is my slave
And Rakhsh my throne, a mace my signet-ring,
A helm my crown ; my mates are sparth and spearhead?
My two arms and my heart my Shah. I lighten
Night with my sword and scatter heads in battle.
Why doth he vex me? I am not his slave
But God's. The warriors called me to be Shah,
But I refused the throne of sovereignty
And looked to custom, law, and precedent.
Do I deserve thy words? Art thou my patron?
Mine was the throne. I set Kubad thereon.
What care I for Kaus, his wrath and bluster?
If I had not fetched Kai Kubad myself,
When he had fallen into low estate,
And brought him to Iran from Mount Alburz,
Thou hadst not belt or vengeful scimitar,
Or might and majesty entitling thee
To speak a word to Zal the son of Sam."
And that:
Ferdowsi's Shahnameh said:
The hero said:
"I need not anything of Kai Kaus.
A saddle is my throne, a casque my crown,
My mail my raiment and my purpose death.
What is Kaus to me? A pinch of dust.
Why should I fear or tremble at his wrath?
Do I deserve such unbecoming words
From one that I released from bonds and led
To crown and throne? Once in Mazandaran
I fought against the divs, and once I fought
The monarch of Hamavaran and freed
Kaus in his foe's grip from bonds and woe.
Now I have had enough; my heart is full;
I fear but holy God."
And yet, he remains loyal to his sovereign, the - to be frank - utterly incompetent Kai Kaus. His sovereign, the Shah, is a bumbling fool who regularly gets himself into stupid escapades. He is at one point convinced to build a flying throne so he can be sovereign over not just what is beneath heaven, but also what is in heaven itself, and then promptly drifts off in his impossible construction and crashlands in the deserts of China. He wages an idiotic campaign against the land of Mazandaran and manages to get the entire army of Iran and himself captured by the White Demon of Mazandaran. In both cases, Rustam has to come rescue him and fix the problems, something which he regularly expresses frustration and annoyance at. But there is no point at which Iran's paladin simply says "lol no" and deposes the Shah. As he says himself, he "looked to law, custom, and precedent" and "refused the throne of sovereignty". Were he to depose Kai Kaus, he does not have any authority to rule the kingdom! Who would follow him? Who would submit to him? He is a vassal monarch of Sistan, not the Shah, not fit to sit on the Throne of Light, even if he might do a better job. Of course, part of this comes down to a degree of divine legitimacy, but in Iranian storytelling, divine favour can be revoked from an incompetent king, as it was to Jamshid, and given to a competent rebel, as it was to Ardashir. And I feel like this really should make the point- there are lots of Exalts who could probably in theory go up and just kill their non-Exalted monarch and declare a new state in their name, but they don't do so because they have some kind of investment - whether genuine or affected - in the system that rules them, or they don't want to, or they might have moral scruples or a million other objections. Of course there are plenty among the Exalted who would do such a thing; imperial Dynasts on campaign, usurpers with dubious yet sympathetic motives that you can fight at the end of an arc and player characters annoyed that their Influence 4 rating doesn't match all their other Merit 5 ratings all come to mind. But it strikes me, at least, as perhaps somewhat unlikely that any Exalt or powerful being would immediately desire to take power wherever they be.
And then you
combine that with the small amount of Exalted people around in the world, the presence of social norms and the fact that many times it may simply be
more advantageous not to topple a king as well as the influence of the divine and the threat of the imperial Wyld Hunt, and I think it all makes a lot of sense.