I agree with you in princple about governers getting exp. It just doesn't make sense that your governer needs to kill 10 bears so that he can "govern" better.
IMO, they should let you build some kind of academy in the city that allows your heroes to train for some kind of gildar maintenance. And then give heroes on the governer path a substantial exp bonus for training in an academy. It would be a good gildar sink, and would allow governers to raise level just by staying in a city.