Simply put, I feel like placing the narrative of "death is the great equalizer" at the feet of the Underworld is missing the point.
(the following is basically my own headcanon, take it with a grain of salt)
Death is the great equalizer in Creation - true death. Natural death; the death that fits within the order of the Heavens. Souls pass through the cycle of reincarnation and - absent the odd case of corruption, once rampant in the First Age but now quite rare - are reincarnated with no care or interest for who they were in life. Whatever great deeds you accomplished, whatever power you wrested from the world, whether you were prince or pauper, mortal or Exalt, in the end it all washes away into Lethe and your next life is fairly ascribed: randomly, with no care for your deeds and crimes.
Now, being fair does not make it good. There is plenty of criticism to levy at this lottery of life; it is no wonder the largest religion in Creation claims reincarnation is in some way meritocratic. And this is where the Underworld comes in. The Underworld is the opposite of that order. The Underworld is unnatural, a corruption of the blind, uncaring fairness of the lottery of life - for good or ill. The Underworld is souls clinging on to what they have, refusing to let go. In undeath you can keep shreds of what you had, tatters of your power.
Oh, it's all twisted and lessened and broken and empty, of course. Your mighty Artifacts are now grave goods, your untold wealth depends on the proper sacrifices being made by your living descendents or your cult. But you can have it all - after a fashion. There is no fairness here, no levelling, no equality. Those who were rich in life set up the rites that will grant them wealth and slaves and magical trinkets upon crossing the great threshold. Those who were powerful carry on a shred of their Essence.
In the end, it's the point. The powerful of Creation refuse to let go; they ape the motions of the power they once held, playing at kingship. The hun ghosts of powerful Exalts, strong in Essence, have powers that echo the most iconic abilities they had in life. In a sense, they pretend to still be Exalted. In death they are Princes of the Earth still, and watch - they can conjure pyreflame from their hands, and their armor looks strikingly like pale jade. They pretend that their nature has not truly changed, that the order of the cosmos has not changed.
But they're wrong. It has. They have.
There is a first thing they dread: it is the bones-deep knowledge that the Essence of ghosts can be stoked, can be made greater. There is no fundamental difference between the nature of an Exalt's ghost and that of a mortal's; the Exalt simply has a headstart. For the vast majority of ghosts, that headstart is all they have: they never stoke that fire, and they die as they were reborn, decades or centuries from then. But anyone who survives, who strives, who seeks the way, can reach heights of power just as great as that of the mightiest ghosts; and indeed ghosts and mortals and divinely blessed are found both among the highest ranks of the Underworld. The fact that ambition works is something the privileged dead fear.
There is a second thing they dread: it is that the Underworld has its own dark mockery of Exaltation, and it too can be wrested by one's own design and drive.
These mighty dead are a great congregation of ice-skaters. Having found a vast lake, freshly frozen, they have begun a graceful and endless dance. None of them realizes how thin the ice, what shapes lurk beneath, none of them hear when the ice cracks and the cold water swallows one of them - and spits them back out.
There is something mightier than an Outcaste Prince hanging on to existence, carrying on echoes of his peerless sword techniques; there is the shade of a mortal hungry and desperate and mad who went too far into the dark and is now a prince annointed in blood, his skin taut and pale, the stars darkening at his passing. When the nephwracks ride on, the shades of the earth's mightiest kings turn away, hide in their chambers, and come out when only the laughter of the spectres remains, carried with the wind. Then they pretend this never happened.
The mighty of Creation ape whatever was the source of their power in life: Exalts carry lesser echoes of their Charms, merchant-princes have coffers spilling with pale ivory coins, warlords lead armies of phantom-warriors that never lived and the slave-ghosts of the servants buried alive with their corpse. But all this is a pale copy. True power is the strength of the Abyss: it is the neverending nightmare below the Underworld, the dread treasures of the Labyrinth, the scentless waters of the Abyss. It is the red surrender, the decision to give in to hunger and madness, feasting on other ghosts until their Essences are part of you. It is the shattering of your own fetters, abandoning whatever defined your identity to become just another monster.
But you need one to have the other. For the power of the Labyrinth, of Oblivion, of the surrender to the darkest hungers, the corruption of all the terrible things a ghost can do to rise above its station - for it to have strength, to have punch, you need the unfairness of Creation seeping through the cracks - you need a pretense of the old order to convey how wrong it is, and how deluded those who uphold it must be.
And there are no great dynasties of Dynasts carrying on their rule in the Underworld, for good reason. Once, the Underworld was considered as a second kingdom, touching Creation, symbiotic with it. The living rose there before their final reward, and some of the Exalted rose as ghost-kings, receiving respect and honor from their living brethren.
And it all went horribly wrong. Because that order was built on a pretense that the Abyss wasn't there, that the darkness didn't seep through and tempt. The cracks showed all the more as Celestial ghosts rose with tremendous Essence and madness and the living Exalts dared not look at them lest they see a reflection of their own cracks. And then they all died and it all came crumbling down. The dead flooded the Underworld in legions unseen before. Ghost-kings who only wielded the illusion of Celestial power were torn apart by throngs of distraught shades who then fell upon each other. All the polite fictions and feeble barreers that kept the Labyrinth in check crumbled. Spectre-lords arose, sarcophagus-cities were carved out of Labyrinth stone with pyramids of iron, nations of the dead perished overnight. And then all the gates and emissaries and sorcerous connections went dark, and for the first time in centuries the Sidereals themselves only knew the Underworld as the Great Beyond, and nothing more.
So now, there is the Immaculate Faith. It teaches that holding on to unlife is a sin, that the best thing a man can do is surrender to Lethe and move on to the next life. It teaches this because it knows that if the Ten Thousand Dragons cling on to their selves, forming dynasties of the dead, a Fallen Realm in Stygia, then it will all happen again. A shining Realm of lie and delusion, dynasties of ghosts whose inflated Essence makes them believe they carry on a shard of their Exalted nature. And the aberrant nature of the Underworld, the fault in its fate, will be the fault in their souls. They will fall, and they will be twisted, and Oblivion will find its foothold once more.
"And in the last eclipse the sea
Shall stand up like a tower,
Above all moons made dark and riven,
Hold up its foaming head in heaven,
And laugh, knowing its hour."
