Chiaki is the type to stubbornly maintain her independence until a sense of duty or responsibility forces her to do otherwise. I always had the idea in the back of my mind that someday Chiaki would be forced to temporarily lead the Lair Legion into some conflict or another (chosen by the LL likely because of experience or knowledge that would save time or casualties), and she would develop a taste for working with the team because of it.

Like since Hatty gets captured so often by big bads to prove a point, perhaps at some point she offhandedly suggests a rescue strategy and Yuki and CSFB! think it's such a great idea they suggest that she lead and execute the plan personally.