Maybe once on the Path of the Governor you would only get Government-related (and perhaps the odd General-related) traits to choose from?
Good general related traits for a governor could be things like:
Over my dead body - +def when defending a city
Best defense is a good offense - +att when defending a city
cunning defender - traps and pitfalls set by the hero cause the sieging army to enter battle with x% less health
Inspiring orator - the charismatic hero can drum up extra militia to defend the city for every battle
An architect trait line might be good within the governor tree, too. Allowing a city to construct (not just start construction, but construct) certain buildings if such a visionary leader is on-site to oversee the project. that might lead to too much micromanagement, but on the other hand it would require more attention be paid to governor heroes than if they are just immobile buffs.
Having a hero oversee the construction of labyrinthine Secret Tunnels beneath my capital that give me a one shot ability while defending that city to summon a unit of militia behind enemy lines could seem cool.
It'd also be nice if having a governor hero present in a city would occasionally generate galciv style random events for that city, decisions to be made by the governor or local issues to be resolved by a skilled leader, that could lead to small permanent buffs to the city or rarely uncover new resources within the cit's influence.