My idea is probably not feasible, but I'll throw it out there anyways.
Champions out fighting gain exp and items but risk getting killed/wounded.
Champions governing in towns don't undergo these risks and shouldn't be given a reward unless a risk factor is involved.
I was thinking of how The Sims 3 handled the random event when your sim was at work. A little dialogue box would pop up and give a few sentences describing a predicament and then the player had to make a choice that would impact the outcome of the predicament, either positive or negative or just plain interesting. If such things could be implemented for Elemental, perhaps it could justify governing champions to gain exp/rewards but also tempered by the risks the ogre-slaying champions have to endure.
For example, a pop up appears in a city when the tax rate has been set to high. A tax revolt is brewing and the champion has to make a decision how to address it: 1) Round up some of the agitators and hang them in front of town hall to intimidate 2) Return some of the gold to placate 3) Address the town and try to convince the people that the tax rate is justified.
The +/-'s on success or failure for the above scenario might be 1) +/- trait for unrest (people are intimidated or not) 2) -Gold (more gold given, higher % of success but no risk/benefit to governor - on fail gold is lost and the same event pops up next turn 3) -Unrest, +governing trait (successfully convinced the people/+unrest, random injury incurred (champion insults mob and gets beat up)
Should a champions stats play a factor for the type of event? I would think it would make it more interesting and entertaining if certain choices for events were unlocked for champion governors with those blood-thirsty, merciless traits as well as those with hippy tree hugging traits.
Also, I think this would give a little more connection to the champions sitting behind the desk, otherwise they'll just be "that dude who gives me +15 gold per turn".