Sir Schwick is right, sometimes there's a breaking point where your empire is unstable enough already, and to add another huge province or region would only tear it apart even more. So you pick stability over expansion, but try to profit from sacking the nearby enemy capital repeatedly. And sacking their capital could slow them down -- so it still benefits you from a competition standpoint.
But I think its effects become more interesting only if you introduce new concepts.
Economic interdependency: international trade IS the foundation of modern wealth. If America isolated itself, it would seriously go to ****. But in Civ, it could isolate itself and STILL be the richest. Civ 4 would need to make international trade give you an extra special benefit -- one that you'd be foolish to go without. This way, having an independant friend across the world would really help you.
Growing pains: anyone who's ever studied history will tell you -- there is such thing as bad growth. If you grow too fast without keeping the masses in check, you run the risk of seeing your nation fall apart. For this reason, Civ 4 would need to have increased dissent in empires that grow, with more subtle and lasting effects than "resistors" and "foreign nationals".
This would encourage some people to say "you know what, I don't need to start ANOTHER occupation, I think I'll just liberate them and let a new AI Civ figure out how to handle things".
Rewards for Altruism: I've sometimes called this "Historic Victory", because the history books around the world in many languages remember you as glorious and, well, civilized. Imagine you needed 100 of these points to win. To liberate another city and give it to a new/old AI Civ would gain you significant points, particularly if they managed to survive without being occupied for a long time. 5 points for liberation, with 25 points if you can really get them on their feet and turning out okay.
For example, Churchill would get 30 points, whereas George W. Bush would get 5 points twice. All of the sudden you'd get people tripping all over themselves to "bring justice to the world" -- which isn't all that unlike how the world is now.
International Culture: I still think it's pretty silly that in Civ 3 you can have a glorious culture when every opposing nation HATES you and refuses to trade or interact with you. People can be tense and still be in awe of your culture, but they need to have their borders open to your ideas, your television programs, your musicians and philosophers, your missionaries, your clothes and wines and silks. In other words, you would actually start measuring the amount of culture that you managed to transmit *outside* your borders, and give you an extra bonus for that beyond what you'd get for culture *within* your borders.
Think of it as a "glass" which might be 90% full with your own culture, but contains 9 drops of Greek culture from the missionaries and philosophers they send your way, and 1 drop of Indian culture from the silks you import from them. This would be very good for Greece and India, with extra special benefit to their cultural victory. In this way, there would be a lot of benefit to liberating another Civ, since they'd immediately have a whole ton of YOUR culture within THEIR borders -- language, customs, values, symbols, ideas.
Nationalism: As much as people can be irritated when their leaders take it upon themselves to be the world's keeper, when things finally go well and are over, people are proud. The way Americans talk about having helped France is something that's a part of their National identity -- that we can fight for freedom, and we HAVE faught for freedom, and that justice is on our side. This kind of national pride manifests itself as actually increasing stability within your borders -- since it helps for forge a national identity.
Suddenly people from Mobile, Alabama feel an intimate connection with the people from Sacramento, California, and the people from Flint, Michigan. You feel like a Nation, because you all have a common thread, a common value you all share: you will stand up for what's right. This feeling in the people is worth its weight in gold. (In fact, next time you go to war, people will remember this reputation for justice, that is if you don't squander it and mislead.)