If other players play the way I do, they almost never choose Path of the Governor. The initial perk (+1 to prestige) is a pretty good one, but if you want to build a champion who can level up, you need a champion that can survive and be useful in the late game. Any other path will offer perks that better reflect that need.
So why not give Governors experience (say, 0.5/season) while they are stationed in a city? They shouldn't level up so fast as to be overpowered, but there should be some way that you can expect to grab more city-buffing traits without carrying the unit to be a spectator in battles. It doesn't make sense how watching a drake get mobbed would improve managerial skills.
I am aware that there is already-ish a mechanic that could do this-- the free XP granted by the Adventurer's Guild. Whenever I play, I find the guild prohibitively expensive, and I don't think I've ever built it. So perhaps it should be cheaper? But I think the more straightforward way is to give free, but slow XP to governors.