Excellent question. I really enjoy attempting to answer it for the sake that I have to reflect on my teaching and my experiences as a teacher to answer it. I think I could write a book on the subject.

I can say that I don't think there's ever a point where any student is completely self-directed. Or at least, I'm not sure how learning can continue if one is devoid of mentors, role-models, or even a competitor.

My most motivated math students are close to being self-directed. Much of the time my motivated students need me to provide some direction toward our next skill or concept of mastery. They'll need me to provide them with practice opportunities and answers to their insightful questions. By insightful questions, I mean questions that show they are very close to mastery of the new concept and have explored it at length, or at least have mastery of the prerequisites of the new concepts on which we are focusing.

I guess basically, my best learners have "grit". Fortunately for my employment, and my personal need for feeling useful, they still do need me around.