[@Raineh Daze]
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[b]The kaiten on its own is a pretty good reason to learn it over most other forms[/b]

The Kaiten in itself I would argue is a particularly poor technique for anyone that doesn't possess any form of extrasensory abilities. For a Hyuuga with Byakugan we know that it's effective, sure, but what if you can't see through the technique? As I've written in my CS, my character will be both blind during the technique's execution and disoriented (dizzy) afterwards. Compared to other "perfect defense"-techniques like Gaara's sand, Kidomaru's Golden Armour or even Hinata's laser-whatever-it-is no jutsu I'd say that the Kaiten is the weakest one if handled by a non-Byakugan user.  

[b]it's a martial arts style that lets you do massive damage with a touch[/b]

Not really. While it does have the potential to do massive organ damage and other nifty stuff you need two things to actually do that properly. One is an almost godlike level of precision, not only because you need to hit pressure points straight on on a moving target that really don't want you to do it, but also because those pressure points are pretty small. This is a lot easier with the Byakugan, but in the end Hinata is evidence for the fact that even possessing a Byakugan and being trained in Jyuuken doesn't make you a organ-shattering killing machine. The second is chakra control. In one of the filler episodes (the arc with the three-tailed bijuu) Hinata is revealed to have chakra control on par with practised med-nins, simply because that's what you need to perform Jyuuken even at her level. 
In conclusion, doing massive damage with a touch is a massive oversimplification. This is not an easy style to use, you need to git gud. A more common style like Gai's and Lee's Gouken will give you great results with a lot less effort. 

[b] I'm just saying that if it's something that can be copied, derivatives would presumably exist in more than one place.[/b]

It can be copied. No doubt about that. The only things in the Narutoverse that can't be copied are the Kekkei Genkai because you actually need the right kind of blood/organ to use it. Jyuuken is a hiden technique just like the Nara clan's shadow techniques and the Kiba clan's dog-techniques. I'd say that the Hyuuga's normal secretive ways, their social and cultural power coupled with their almost godlike efficiency on the battlefield has made sure that most people who actually has seen enough of the style in action to even try to create a derivative will be persuaded not to do so.

[b]it just seems bizarrely unlikely that the defector would be a Hyuuga, then have the rest of the family do nothing about it.[/b]

Unlikely, sure. But not impossible. I have intentionally not made any decisions about the Saizen's background. For one it'll be much more fun to experience that in the game, but I also do not want to accidentally ruin any of the GM's plans. Besides, she could probably fake her own death like Madara if she really wanted to.

[b]The rest of the family, mind, apparently letting either some sort of genius go or the main branch--since, hey, Kaiten isn't part of the basics.[/b]

Do keep in mind that before Neji showed of his talent at the Chuunin exam no one in the clan had any idea that he could do any Jyuuken techniques at all. Yes, the clan that prides itself on seeing everything... Had no idea.

[b]And then this advanced part is perfectly copiable?[/b]

No one has said anything about it being perfectly copiable. On the contrary I've stated several times that the cult's version only looks like Jyuuken, bur is not as effective as the original, even in this very post. Even in my CS I state that Jin gets a boost in force which equals a full fist, not any kind of organ-damaging penetrating power. The result of Jin's technique is a mix of Jyuuken (for style) and Tsunade's or Sakura's enhanced strength specifically applied as power-pokes. 

[b]It's a really convoluted train of thought for one ability.[/b] 

Convoluted? Which part are you having difficulties following? I might agree to far-fetched, but I believe that I have explained the theory quite clearly. Also, it is not about one ability, it is a fundamental part of the character. The fact that the techniques are replicable impossible to master perfectly serves to raise the ideal of the first Saizen to a level which is unattainable for the character, thus proving to him that she is godlike. If the Saizen had used another set of abilities this would not have the same effect as mastering the techniques may be outright impossible to begin with or simply as possible as any other technique.

[b]Also I do worry about having a character with some sort of familial obligation to kill a genin. That's just awkward.[/b]

You might worry, I see a great foundation for drama. 
Will the Hyuuga really go for the kill immediately or will she suspect that there might be others? 
Will she actually deem the technique as close enough to Jyuuken, and thereby admit that even a low-life such as he can come close to her own perfection?
What will she do if she can't go for the kill? What if Jin's jounin is nearby? What if that jounin is stronger that the Hyuuga? What if Jin has some kind of important diplomatic function, and killing him will have dire consequences? 

These are just some of the questions I can think of at the top of my head. Interesting, eh?
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