You have several interesting thoughts about studying bugei, including a comparison to other sports, namely basketball. The parallel you draw between needing a teacher to progress within a martial art and not needing a coach to become proficient at basketball is skewed at best.
Whether one is a called a teacher, coach, or trainer, is a matter of semantics. His job is still the same, to instruct the player or budoka to become better and ultimately to win. By eliminating bad habits, emphasizing basics, instructing the student in advance techniques or plays, and helping the player frame the correct state of mind, the teacher/coach allows the student/budoka to excel.
You claim that a person who studies hard (presumedly on their own) and has the prerequisite talent can become an expert swordfighter. I would like to see that person fight with a challenger who has studied the same amount of time with proper training under a kendo(add your sword school here) instructor. I would be willing to bet that Prof. Friday's fighter would lose.
You're correct in this Professor, quality training IS about the path, not the goal. Studying hard at whatever you choose will result in learning about yourself and others in the process. By training properly with guidance, correction, and sometimes punishment (several laps in shiko, or receiving a D for poor effort on an exam, or losing a game), the student/budoka becomes a winner.
Yes, at some point the student must cease being a student and strike out on his own. To teach others what he has learned. And given time, that former student will develop his own style, perhaps completely different from his original teacher's, but the lessons learned, the basics taught by his instructor, will become a solid foundation upon which the former student/new instructor can build and grow.
Individualism should always be encouraged. Take your teacher's aikido/basketball and make it your own, but there should never be a replacement for a quality teacher, for there's always much more to learn.