AoW2, Shadow Magic, and MoM essentially made the sovereign a non-combat unit. In the AoW series you could put the sov in battle, but they didn't level and weren't strong at all. In both games they were the only units that seriously cast spells. This made them really special.
I don't think they want to go that far in LH, but it does seem there needs to be something inherently special about the sovereign. They are heroes with a head-start right now. I would be interested in ideas about how this could changed without radically altering the gameplay.
How about bringing back sovereign essence for some purpose, maybe to perform a limited number of "miracles" of some kind? They could be like sovereign-only spells, but not tied to the magic system. But call them something cool, like miracles. They could make cities more fertile, give more essence slots, make a resource appear, infuse champs or units with some kind of power, ect. Maybe they could focus on making certain aspects of the empire building stronger, research a technology instantly, or they could do devastating things in combat. That way your empire-building is more directly tied to the sovereign. "That's why that guy is in charge, he turns swamps in to gold mines."