I think rebel clans exist purely for the player to have an easy entry into fief ownership if you do not want to go the long slog of joining a faction, waiting for a fief to be awarded, waiting, waiting, till you rebel yourself and start your won kingdom; or play the politics and wait for the current faction leader to die and hope you have enough influence to become faction leader.
Rebel clans give you a way to dive directly into your own city state, and then start building your faction.
In my current game, I remained mercenary, working for several factions to build relation, and when rebel clans emerged, would pounce on them before the faction could get around to deal with them. In short time I had three such fiefs, not too far apart, and then declared my kingdom, and started the expansion project.
Easy. Low hanging fruit.