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 am interested in ideas about how this could changed without radically altering the gameplay.

How about bringing back sovereign essence (way back from WoM) for a different 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. Miracle is a good name, and maybe you can perform them at certain points in the game (they cost something that regenerates). 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. In addition to being a hero with a head-start, the sovereign performs miracles that directly benefit the empire strategically. "That's why that guy is in charge, he turns swamps in to gold mines."