Worlds in the Periphery are normally defined by two points: First, they are very far away from Terra. Secondly they tend to be very underpopulated. A periphery world is often a backwards pirate's nest in large part because there is not enough people living there to build or maintain significant infrastructure. There is also some mention in canon that the farther you get from Terra, the number of worlds with ideal Earth-like conditions drop considerably, making it hard to build a mini-empire when you might have only one bread-basket world out of a hundred, and few jumpships to transport goods around on a reliable basis. So it makes sense the Successor State rarely muck around there despite their tremendous might and the potential opportunity to find a resource-rich world to exploit; it is just too costly in most cases to even throw a single mech lance at it.