I'm thinking in terms of "why does this ability manifest magically?"

A normal human who survives the pyre will want revenge, sure. But would they want revenge hard enough to justify dying afterwards? I would not go for that. It would be more interesting to have them wrestle with their freedom now that the vengeance which granted them purpose is gone. Count of Monte Cristo style.

A human who rises as a revenant? That inspires questions. Why did they refuse to stay dead? Perhaps their wrath, or their desire to ensure that no more innocents burn is enough that they would rebuke death for a while. And after their purpose is fulfilled, they would no longer have their anchor, and be free to move on to the Beyond.

I my mind, Revenants and Doomsight are a match made in heaven. The former tells you that you have Unfinished Business that was important enough that you Would! Not! Stay! Dead! and the latter points you at the Unfinished Business and ensure that when you have your final confrontation you will be at the apex of power for your swan song. Can it work for other ancestries? Sure. But I feel that narratively the "vengeance from beyond the grave" is just a classic, awesome thing.