Ben the request-meister asked for "A specification of a game that you would love to play but hate to make" or vice versa. Here's a sketch for a game I'd love to play: a fractally-scaling societal sandbox that combines the best of Civilization, Dwarf Fortress, Spore, Adam Cadre's IF game "Varicella", and the Grand Theft Auto series.
The sandbox scenario is that you're an alien civilization making contact with Earth. You choose a few startup parameters:
- What you look like, on the Star Trek scale of alien weirdness: El Aurian->Andorian->Horta->Medusan
- The size of your party: individual->small party->large party->army
- When you arrive at Earth: ideally any time in human history, but I'd settle for selected times within 50 years of the present.
- How much more advanced your technology is than 21st-century Earth's. Maybe higher levels here are something you have to unlock. I suspect higher levels would not make the interesting goals any easier to reach, but they would certainly make the game as a whole more interesting.
- An ideology for your party (see below).
- One of two scenarios. In the vanilla scenario you start off with one ship in Earth orbit, all your tech works, you can move around the solar system, and you're undetectable unless you break radio silence or otherwise reveal yourself. In the "dammit" scenario your ship has crashed somewhere on Earth and been damaged or destroyed. In this scenario you start with little technology, possibly not even your universal translator.
And that's it. You're weird, you've got advanced technology, and you encounter or are forced into human history. You can try to help humanity (for whatever definition of "help"), make and sell stuff, conquer the planet, try to blend in, try to be accepted, or just repair your ship and get out. The levers of society are exposed to you at all levels: personal relationships, trade, diplomacy, media and propaganda, espionage, etc. You can play it like an RTS, a wargame, a game of stealth and guile, or a tourism ungame. If you play it as a wargame you've got a political wargame, because the tactics you deploy are in the service of some larger goal.
All the time you're controlling some specific member of your party. You can probably switch between party members, but there's never, say, a disembodied RTS interface: it's you giving orders to other people. If Bob gives an order, it affects Bob's reputation with the people who see him do it, the people who carry out the order, and the people affected by the order. If humans see any part of this, the part they see affects your whole species' reputation.
Ah, reputation. Humans' ideologies are well-known, but alien ideologies can be different. The player's actions will be interpreted by NPC aliens (if any) through the lens of the party's ideology, which might make them happy or unhappy. One thing that might make them happy is converting humans to their ideology. Ideologies would be selected from a list, or assembled piecemeal a la Credo. For some ideologies it might make NPC aliens happy to convert NPC humans to some other ideology; a master morality/slave morality thing. The game's sense of morality is intersubjective rather than objective. There's no "you can't do that" enforcement mechanism; rather, a gradually increasing NPC resentment at having to follow orders they see as unethical.
I'd hate to make this game because it would cost hundreds of millions of dollars (GTA4 cost $100 million) and it would be insanely complex, possibly requiring something close to strong AI. While writing this description I thought about recasting it as a role-playing game, but I can't see it being fun to DM. If you gave the humans a more active role you might be able to have a human team and an alien team.
A variant that might be easier to implement is to switch it around and have humans make contact with aliens. It's easier because you don't have to simulate the alien societies in as much detail. People accept ahistorical and culturally homogeneous alien species without thinking much about it. But it wouldn't be as fun to play, since one of the cool things about my idea is the way it lets you try to manipulate humans on any level.
 I don't need to be able to switch to any given member of my army, but in a very large party I'd like to be able to switch to certain archetypes: the leader, the leader's lackey, the guy who runs the media/military/trade operation, the grunt carrying out the media/military/trade plan. People who interact with the humans on any level; no middle managers who are only concerned with other aliens.
 The party might not have one fixed ideology; maybe a cruise ship crashes on Earth and the passengers and crew don't get along but they've got to work together, like how I imagine "Lost". Party ideology is just a baseline for personal ideologies. Similarly for humans. You can always find one scummy human who'll deal with you no matter what you do, but if you need a bunch of humans, you'll need to cater to human ideologies or use force.