The best answer to this line of questioning is that, contrary to their appearance of just another cult that wants to destroy the world, the Mythic Dawn (as the name implies) wishes to up-end the existing order and return to the pre-existing order (or, rather, non-existent order) of the Mythic-Dawn Era, a time when time was non-linear. From the UESP:
The new land is a chaotic place where time follows no clear path and creation is constant, following a downward spiral that causes levels of existence to create lesser levels beneath themselves. This results in the dissolution of many spirits and the creation of mortals, whose memories from this time result in their creation myths.
To strengthen this idea, one need not look further than the Mythic Dawn's own Commentaries, which are laced with Mankar Camoran's words idealizing this era as one in which anything was possible, freedom was complete, and only free-will reigned.
"Let all know free will and do as they will!"
You, brother, are to sit with me in Paradise and be released of all unknowns.
I crave not your downfalls, though without them you might surpass me even in the coming Earth of all infinities.
Once you walk in the Mythic it surrenders its power to you. Myth is nothing more than first wants. Uhokerrable truth.
Understood laws of the arcanature will fall away like heat.
CHIM. Those who know it can reshape the land. Witness the home of the Red King Once Jungled.
You, brother, are to sit with me in Paradise and be released of all unknowns.
I crave not your downfalls, though without them you might surpass me even in the coming Earth of all infinities.
Once you walk in the Mythic it surrenders its power to you. Myth is nothing more than first wants. Uhokerrable truth.
Understood laws of the arcanature will fall away like heat.
CHIM. Those who know it can reshape the land. Witness the home of the Red King Once Jungled.
etc...
But as we know, this Mythic Dawn Era that Mankar gets off over came to an end with Convention, where Aka cast himself onto the earth and imposed his laws upon it. As the UESP says:
[Akatosh's] full presence causes all spirits and chaotic forms of creation to crystallize, and time becomes linear and ordered.
And then Aka said: "Ho Ha Ho."
For to impose linear time upon Mundus, Aka imposes his law as the epoch-eater, Alduin. For what does linear time mean if there is no beginning nor end? So he must eat the world to preserve his law and bring order.
"You stupid little f*cker, do you even know what would HAPPEN if that happened, my dying and being unable to eat and the kalpa left to run forever?
Apparently, he may have.
But there are those who oppose what Aka has done. Lorkhan, who throws his heart to the Star-Wounded East, with which normal men could become gods. And the Demon-Leaper, who with Lorkhan and with his servants hide pieces of each kalpa with the intent of destroying Alduin and ending the cycle of destruction.
These servants of the Demon-Leaper will, like the followers of Trinimac, will be transformed with him, becoming the Mythic Dawn, whose millenniums-old conspiracy to release Dagon on Nirn so that he may break his curse by destroying that which keeps him imprisoned, so he could reclaim his protonymic identity, Lehkelogah, Demon-Leaper and King; so that he may again conspire to end the eating at the end of each Kalpa.
Mankar and his Mythic Dawn, at least from what can be gleamed from the commentaries, find this cycle to be slavery, and Aka's supporters to be contemptible. It is, in their words:
Recorded, the slaves that without knowing turn the Wheel.
Enslaved, all the children of the Aurbis As It Is.
Enslaved, all the children of the Aurbis As It Is.
so shall he crack the serpent crown of the Cyrodiils and make federation!
Camoran even warns of the destruction that will come with Dagon's return, but reassures his followers of the ultimate goal.
Night follows day, and so know that this primary insight shall fall alike unto the turbulent evening sea where all faiths are tested. Again, a reassurance: even the Usurper went under the Iliac before he rose up to claim his fleet. Fear only for a second. Shaken belief is like water for a purpose: in the garden of the Dawn we shall breathe whole realities.
Strangely enough, Mankar may even be a Dovahkiin, given that he could wear the amulet and speak in tongues, spouting fire as he did so.
Offering myself to that daybreak allowed the girdle of grace to contain me. When my voice returned, it spoke with another tongue. After three nights I could speak fire.
It may be simply metaphorical, sure, given Dagon's connections with that element. But from tentative hints like these, we start to see not only the Emperor of Cyrodiil, representative of Akatosh, as the Mythic Dawn's enemy, but the mythical God of Time himself.
To further push this line of reasoning, the Commentaries may even give testament to how Dagon, as Demon-Leaper, tried to stop Alduin's eating all those years ago.
"And the Greedy Man always waves his arms about around this time as if to stop me just like you. It is almost as if you two work together to delay me. Is that what this is? Is some other low spirit hiding portions of the world while you two do this thing? Is this why the kalpa-feast always takes a little longer than it did the previous time?" - Alduin
Deathlessly I intone from Paradise: Mehrunes the Thieftaker, Mehrunes Godsbody, Mehrunes the Red Arms That Went Up! Nu-Mantia! Liberty!
The way the Commentaries ties Lorkhan and Mehrunes together also echos the Seven Fights, although it remains a mystery as to what SCARAB AE AURBEX (Lorkhan is ????) means, or how he is tied to the Mythic Dawn worldview. Others have said that Mankar Camoran claimed Mundus to be a daedric realm of Lorkhan, though exactly how this is outlined in the Commentaries is unclear to me. Any aid here would be nice.
So... that's it. Scatter-brained, to be sure, but what I wanted to do was display the connections I was seeing between Seven Fights and the Commentaries after finding myself wondering who these "lesser spirits" were that were helping the Demon-Leaper King and the Greedy Man hide pieces of Nirn in hopes of destroying Alduin. It would also be *deliciously* ironic if the player winds up on the same side as the Mythic Dawn in Skyrim.
But, I await your comments.