I can't imagine any of the queens becoming anywhere as powerful as Kerrigan in foreseeable future (especially if she consumes hybrid essence). However, I think she wants brood mothers to compete with each other (like Primal Zerg) for the position currently held by Zagara (a CEO, essentially). It will provide an outlet for aggression and will benefit the Swarm by encouraging evolution.
I don't think she's trying to get them to compete in that sense.
If she did that, then assuming she leaves the swarm, Za'gara takes over. She's the strongest broodmother, so all the other broodmothers immediately obey whatever she says, and that would make the whole swarm command structure exactly the same.