To me, the role of kings or mayors would be to have an NPC that does nothing but consume resources and get in the way of everybody else who is doing real work. At least that would be the way I’d put it into Stonehearth if I was writing it in as a mod.
It would even serve a function in terms of “keeping the economy running” where other members of the village would have something to do by supplying items (like furniture, a house, weapons, statues, etc.) for the mayor as a form of taxation. The mayor in turn would “tour” the city and check out what everybody is doing as a good politician, but generally be in the way as they would need to wait for the mayor to move if he is standing in front of the forge or in a storage area. Basically a general nuisance.
On the other hand, in battles the mayor could be leading the armies while wearing “the best” of what the village has to offer… therefore being a prime target in any battle arrangement. If the mayor dies, some other random villager (or perhaps selected by the player) can become the new mayor.