Interesting. You presume yourself qualified to make such a determination.
People have automatically assumed that the Sharingan came from the Byakugan. Cause if your going by what Kakashi said then thats what you're saying about the eyes. If your saying, " Byakugan came from the sharingan".. then you have no manga proof what so ever.
Kishimoto has already invalidated most of his own Manga. It's a fool's errand to draw any kind of conclusions about what is or isn't possible from the canon.
So, far only eyes known to be related are Rinnegan and Sharingan.. well the sharingan isn't actually directly leading to the rinnegan, since the Senju dna is also required. But eye wise those are the only 2.
Honestly, we don't -know- this to be fact. A couple of self-important narcissists hold this opinion. As one, myself, I can attest that my opinions in regard to my genetic superiority to everyone else are based purely upon rampant speculation.
People all kinds of weird theories about Byakugan... yet the only thing it has common with the Sharingan is whole chakra seeing thing.
The exact visual prowess of the Sharingan is a bit obscure. It's stated to be capable of observing every minute detail that makes it very difficult to defeat with genjutsu and almost impossible to defeat with taijutsu (as movements can be predicted accurately). Some descriptions mention a sort of "chakra aura" - but it's rather vague. Originally, the whole idea was that the Sharingan could copy and remember complex sequences of hand-signs. Then it became overpowered with Tsukuyomi... and now it's so ridiculously out of control that the next ability of the Sharingan will, no doubt, be titled: "Kami."
If the Hyuuga were any relevance to the Elder son they would've been mentioned and would've been important to Oro or other villains.. but clearly not.
This is a sort of yes and no scenario. The Hyuuga deliberately created the Caged Bird Seal as a form of protection. While it's often portrayed as a form of oppression - the only Hyuuga worth capturing are Main Branch members - who are skilled in their own right and solidly protected by Branch members. If one were to capture a Branch Hyuuga - the seal is activated and it destroys the critical components of the Byakugan.
Further, the main villain focus on Sasuke is from Orochimaru (who wishes to have Sasuke's eyes to aid him in unlocking a much wider range of jutsu - something the Byakugan is, for whatever reason, not as effective in this role) and Tobi/Madara/Obito/schizophrenic pedophile - who is a surviving Uchiha with a narcissistic god complex.
Point being - most of the villains that the canon story has focused on only had reason to be interested in the Sharingan.
That said, if there does become renewed focus on the Byakugan... I'd appreciate it if Kishimoto keeps it toned down. The Sharingan is so ridiculous that it's not even funny, anymore. The Rinnegan is, as well... all I needed to hear was: "The Sage was said to have created the moon." ... You know what that means... Naruto's destroying it in order to prevent the Eye of the Moon from being completed. Nine-Tails Hate-Cannon into the moon - massive explosion - problem solved.
Another stupid comparison is this:
Uzumaki is to Senju,just like, Hyuuga are to the Uchiha..
UH HELL NO.
Well, depending upon exactly how you interpret it... All ninja are said to have descended from the Sage. Whether you interpret that as all Ninjutsu descended from the work of the Sage... or all Ninja literally descended from the sage... the the lore is not very well expressed in the series with different characters stating different things and coming to different conclusions.
Obito (Madara - as that is who he got his information from...) is just another voice among the legends. The only reason people take his reasoning any more seriously is because he has an eye that can do everything but replace a can opener. It is very well possible that there is a link he'd rather not acknowledge.
Or is simply unaware of.
Honestly, I don't think Kishimoto even knows. It's evident that he's well beyond the plot as originally envisioned and is flying by the seat of his pants. Whether or not we get any kind of update on the lore of the Byakugan will depend upon how large of a role Hinata and/or Neji end up playing in the end.
If they end up playing a large role for some reason or another (such as another Hinata sacrifice scenario) - then it's likely some relationship will be drawn between the two. Otherwise, it's unlikely that Kishimoto will bother.
Since that would necessarily thicken the plot and lore, I honestly doubt Hinata or Neji will end up playing much of a role at all in the end. Despite the fact that the lesson of Naruto is that "you can't do everything by yourself and take on everyone's burdens without help" - that's exactly what Naruto will do, and he'll Leroy Jenkins right on through.
So all we will be left with is speculation and no real answer. So no one can really have a more or less justified opinion.