Curse of Doom gets no buffs from runes?

If Curse of Doom is going to be considered a DoT, shouldnt it also benefit from Haunt being active? If it is not going to be considered a DoT, shouldnt it benefit from Mark of Chaos?

I’ve been messing around with CoD and have found that talented agony casts by themself hits just about as hard as a CoD cast in the 1 min window (allowing for pandemic). Adding in Haunt there is no comparison for the damage between the two. Haunt atm does not seem to impact CoD in any way.

With a new rune focusing on Soul Fire, should Curse of Doom be looked at as well for being worthy of being cast?

I really dont have a suggestion for it, just noting that Curse of Doom has no damage use in season of Discovery outside of hoping for a Doomguard proc and hoping that doomguard doesnt kill you. I am using the test gear and some ST pieces. However with improved gear all spells should be improved. As is CoD only languishes the better your gear gets.

Day later edit-
I took the time to get a Zila Gular trinket from the fel portals. I just checked this with use for Curse of Doom, it does not seem to work with the trinket. Is there a reason that it would fit the description for use but not actually be usable?