The most satisfying idea i came across with them is that they would force the player to toy with food growth, health and culture to have a balanced empire, because the more satellite cities you would have, the more they may differ from you culturally, split up and stop your expansion.
So either you could : reduce your growth, increase your health or increase your culture, and building roads mainly. (for a deeper penetration of your culture) Of course reducing your growth sounds sub-optimal, it would be better to keep a high growth, while raising drastically one health and/or culture. If you raise your health, you could have bigger cities, hence less fast expansion of self-generating cities, and if you increase your culture and build roads, your self-generated cities would be well integrated in your empire faster, keeping them from spitting up. (and stop your expansion in that direction)
Basically health would be for tall play, culture for wide, and the two being mutually exclusive ! (as long as you concentrate on health or culture, and a mix of the two would result in a mixed bag, with same potential !)