Why did Horikawa Kodo not take the boy under his wing and teach him everything he knew? Ok, maybe he tried, and Tokimune refused - that's a possibility. Maybe he thought that if his Sokaku wanted that, HE would have taught him. But somehow, I don't think that's it. Another puzzle without an answer.
While I agree the answer is most likely unknowable, I would suspect some of the teacher/student relation could have strongly been at play here. My own sensei is generally a product of teachers from roughly the same period, and while he is modern enough to know that much of that wouldn't fly today, he still relays to me a lot about the dynamic of what he experienced in hope that some of us try and adopt some of that mindset ourselves. I recall one story where one of his teachers, a very senior life long kendo and Itto-ryu swordsman actually broke protocol and asked sensei (by this point an instructor of Goju-ryu karate by profession running his own dojo) to check him the Sanchin kata as he felt there was much he could learn from the breathing methods included there. While most of us in the modern audience would admire this teacher for not resting on his seniority and wanting to learn something of value, even if from one of his own students, I was told the reaction at the time was one of shock. Supposedly my sensei was aghast that his sensei would even suggest such a thing and flat out refused saying that it was inconceivable that the student teach his teacher. He would also tell stories about how if his sensei was asleep everyone would have stay awake and "guard" him as it were (such demands were of course never made, but it was the student's duty).
While I've never looked closely into the issue, it seems to me that most of Takeda's "senior" guys all were very proper in their relationship with Takeda (Ueshiba was famous for it), and I would have a hard time imagining any of those guys taking the step from helping out Takeda's son to actually "teaching" him. Maybe if Takeda had died, but he was still floating around and had a habit of showing up completely at random. If I remember correctly, he got quite upset at some of his own students for teaching their own kids (although those "kids" did alright in the long run under Sokaku), so I could only image the reaction if one of them got caught teaching Sokaku's own son behind his back. But in the end who really knows. The human element at work between all these people makes it seem to easy to me to say that this was the only factor at work here. (shrugs)