But Merlwyb is regarded as the greatest admiral they've had and Mistbeard, former pirate king, follows her because he knows she's better?
Nanamo's entire story arc is that she's young, naive and inexperienced and literally every other person is trying to take advantage of her because the sultanate for generations has just been a puppet position. Raubahn leaving her is the kick she needed to actually grow up and manage things on her own, and we'll see how that evolves over time, I imagine.
Guild leaders don't really matter much as they're often academies with the occasional official business side. Not every school will be headed by the absolute best in the field. As for the gladiator one, since you specifically called it out, she was chosen because she's more honest and disciplined after the former guild leader was revealed to be a cheater who took bribes and bet on his own matches. Sure he might be a better fighter, but we don't know for sure if he's a better person.
That said, I think this has strayed very far from the point.