I don't think it's meaningful to think much in terms of families when there's only one character per island, except perhaps for those families who habitually acquire power. The sense of a family inheritance or of a younger generation serving in the ranks whilst the older wields political power requires either a lot of RP or more than one character.
You've never seen a Kabrinsky at work then. Even now that name causes those in power to shudder in fear on Dwilight.