Doom - a downward spiral
The path a Hero of Doom treads is bleak and pessimistic, following a nearly constant downward arc with little exception. They are beset on all sides by disasters, and their attempts at rectifying these carry heavy costs. Nearly everything Sollux does is an attempt at averting disaster, and these attempts often carry heavy costs. He creates and plays the game in an attempt to save his species from extinction, he saves Feferi from meteors (losing his life in the process), he fights Eridan to stop him from joining Noir (losing his sight), and he sacrifices his life again in Cascade to get the meteor to the Sun (and away from Noir). At this point Sollux bows out, removing himself from any significant role for the rest of the story (though a splinter of him is later brought back in Erisolsprite). Given how his story had gone up to this point and how little he had left to lose, this was probably for the best. Perhaps, as a Mage, a knower, knowing this was why he chose to do so.
Mituna’s part in the story is smaller, but he too is beset by loss and disaster. As the Ψiionic, he faces loss, being enslaved by the Condescension and reduced into a ship’s engine. As Mituna, he faces disaster, as (according to Aranea) he had his multitudinous prophecies of doom ignored entirely, and ultimately sacrificed his powers and much of his sanity.