+1 Prestige can be attained one of seventeen different and easier ways, and is a relatively opaque bonus at that (which is to say that nowhere does it really indicate what +1 prestige DOES for you other than "your empire grows 'faster'").
We are not asking for free exp, nor free gold and prizes. We are asking for a system that WORKS and MAKES SENSE. The current PotG doesn't make sense and doesn't really work. Make it go away or make it work. That is all anyone asking for changes is asking for.
We can do the "retired busted up hero" thing, but that's a whole other layer that the current system isn't prepared for. We can do some manner of production-based xp generation and a better (read:legitimately useful) set of traits, but that seems to send you into a tizzy about how they are getting free exp. Alternately, we can totally do away with them and dream up some other fifth adventuring class which shares other components of the four and waters their identities down further. Whatever. PotG doesn't work as-is and needs to change. Agree and let's move on.
Actually, prestige is a rather scarce resource. There are only a select few sources, the biggest of which is your sovereign's level (divided by two), which is why "collecting" surrendered sovereign is so powerful. Aside that, you have a couple (literally) of techs that gives it, and a few buildings, most of which are 1 shot wonders (aside from the almshouse that you have to select for lv3 cities and have to give up other useful choices). Most of these are actually quite hard to get early game, when the 1 prestige makes the most difference, because your global prestige is divided by the total number of cities you own, and becomes the cities' base growth (I don't know why you say that that's opaque?). So early on, if you have 2 cities, turning that first hero into a PotG is essentially the same as building an inn in both of those cities (and it's not that hard to get to level 4, especially when you can recruit them at lv3). This makes PotG very powerful in that early portion of the game. If you manage to do it for 2 or 3 heroes, you can completely outgrow your competition, and since population affects research and production, it soon results in a steam roller effect as long as you can keep expanding. I suppose you can argue that it needs better documentation or explanation, but this bonus is definitely not something to scoff over.
Then, if you want, you can level them a bit further, they give monetary and research bonuses along with administration. All of these are powerful early, and not quite as useful later, so you could argue for some kind of percentage base bonus (maybe for the 3rd trait?), but I certainly wouldn't call them broken or needing to be toss aside. I mean, honestly, the biggest influence on your combat abilities is the equipment you wear anyways. If you deck out a governor in awesome gear, they will still be a force to be reckon with. It's not like you suddenly become completely useless the moment you select PotG. Even without the great battle gear, they can still cast spells, buff/debuffs, etc. I'm not sure why you feel like it doesn't work and needing to be tossed out, but I sure don't agree with that mind set. To me, PotG is something that is powerful early, but becomes less useful later on... and that's okay. If you don't want to give up something for those early bonus, don't choose it, there are four other paths to pick from.
The biggest problem I see with people suggesting things like giving PotG free exp per season, or exp per things built, is that I think it would essentially turn all PotG into city guards. It's like they got hit with an arrow to the knee and retired. Heroes are meant to be wandering the country side fighting stuff and doing heroic things, not watching stuff being built. I don't care if it makes more sense, it's terribly boring, and that's bad in a game. That's why I kept saying that the problem lies in the administration line more than it does in the path... but I'm not going to go around suggesting it be removed just because I don't use it much... unless I start with Bannon.