In my dream world, we'd have both something like an Advisor's Council to help a channeler deal with the realm as a whole and some settlement-leader slots (administrator, viceroy, whatever) where champions could work to help a specific location.
Settlement-Leader slots...Champions performing civil services.... I like it! 
imagine the tactical depth you could make on the world map! Sending a hero with unique single-city oriented bonuses to key cities would provide interesting decisions. Should I put my hero in my "army factory" city to boost the troop production rate or should I send him to protect a vital outpost on the frontier from enemy incursions.
Of course, people could build a ton of champions whose only job is to act as administrators would cause a balance issue. How to solve it, hmm....: 1.) Naturally heroes will be more expensive and their primary role should be fighting in battles. 2.) a Skill/Level System where a hero starts out being junk and progresses into a master. 3.) Champions should only be assigned to one task (military, social, research) at a time. 4.) limit the number of Heroes that can be assigned the a specific task in a specific city or limiting the number of Heroes that can be administrators in any given city. 5.) limit how many heroes can be place in administrative roles.
As long as having a certain military advisor doesn't have the people prevent you from going to war
I would imagine that would help stop the annoyance one gets when one wants to go to war in Civ 3 and 4's late games. Let's call this advisor Prince Humperdink (I think that's how his name is spelled in "The Princess Bride") who does just this, make your people actually want to go to war with a hated enemy.
I like your idea, Landisarus, about how these governors or council members should be more than just stuffed toys that are only used at the beginning. How about having them periodically hold a meeting to say their opinions on how you're running the kingdom like militant advisors would lodge thoughts about your military, foreign affairs officials and merchants would talk about diplomacy and trade, researchers would naturally discuss the quality of research, and so on. Heck, they could even have some witty banter between them (like the king of thieves and the chief magistrate would vocalize their dislike for one another) some of which could be used as comic relief.
Examples: 1.) The King of Thieves complains about how there's too much law and order and his people can't make ends meet and the Chief Magistrate just chuckles and says "no problems here". 2.) The Militant adisors all want to start a war with a rival faction but the merchants and diplomats want trade agreements and an alliance with the same faction.
Naturally, if you choose all militant advisors you would shut yourself out from the advise of diplomats, merchants and others. So you would have to choose carefully what you believe is more important. Thus creating another balancer.