On the topic of governors as "Great Administrators" -- A couple options
1. Wouldn't it make as much sense for you to be able to convert Great People into Governors? Generals might become a Castellan and Scientists might become an Educator. This would more likely mean that they would each come with their own flavored Governor Bonus, just like they each have their own special action right now... presumably they decided against this deliberately, since it makes as much sense as what they did, it just must not be what they wanted.
2. Otherwise, Great Administrator points would probably come from normal buildings and government Policy. An Economic policy might give you GA points for every Market, or every Temple, Library, Forge, Barracks, etc. These are all things that need administration anyway, and policy would cause the best Administrators to be nourished and rewarded, becoming Great People. Plenty of Wonders would likewise make points as big expensive projects need equally good ongoing management.
3. Tangentially, it would be interesting to retire Great People and have them become your advisers (in the Civ II sense) instead of governors or special effect fodder. It would be fantastic to be able to say that Albert Einstein is my own personal science adviser, rather than just immediately spending him to get whatever his reward is, or sticking him in charge of some troubled city somewhere. That's a lot of portraits and dialog to research and create, but it would be really fun to have as a player.
I won't claim that what follows here is a good idea, but it came to mind:
Way back in 3MA #51 Rob, Troy, Tom, and Bruce talked about alternative ways to think about research in games, and one of the things that stuck in my head since I first heard the episode is the idea of non-guaranteed science progression, that is, sometimes your scientists are just shooting in the dark and aren't making steady progress towards a technology that has never existed. The idea comes to mind that technologies may start hidden; research boosts would reveal them, and great people or other events would also reveal them, but without knowing that a tech exists, your science points can only slowly or randomly build up technologies you haven't yet revealed, eventually "discovering" a technology at random. This also has a built-in rubber banding, if you discover that technologies exist through trading partners and diplomacy (perhaps you can offer either tech knowledge, or a tech boost, on the trading table), through espionage, or through the advancement of Ages (previous Age tech is always known?).
It comes to mind because I imagined that the advisers above were the ones that unlocked things; I imagined you started with no Advisers, but having a military Adviser informed you about Military Tech, and a science Adviser gave you education tech, etc. I suppose there might still be a few hidden and you'd need to rotate your advisers on occasion to reveal them, or else continue investing in blue sky research that might not pan out.
It's an idea that would need to be massaged and played with--it would be a very radical change and might be better as a mod or alternate game mode because a lot of people would chafe at having that kind of choice taken away from them. But it is an interesting alternative with a lot of room to poke and prod at things.