It's just a conclusion that we arrive at when analyzing the traditionalistic characteristics of the clan and the self-importance that they assign to their doujutsu which its physical reemergence in individuals of the Hyuga bloodline would likely be impacted in some form if Kishi's comment about a hypothetical Hyuga/Uchiha hybrid possessing only one eye of each KG is anything to infer from; this fact alone would prohibit the character from naturally acquiring a dual EMS or any additional MS techniques than the one granted by the single Sharingan eye. You could just attribute these thoughts to presumption though as the Hyuga do give the impression to some readers that they are the sort who would make it an effort to preserve the continuing prominence of their KG within the family and their identity in general (similar to the Uchiha).
I think that while that conclusion is interesting, it is also not very substantial because:
- In real life, eye colour is determined by eight different genes, with 37 variations of these genes (in other words, people with the same eye colour can have different genes).
- That theory will only work if it is assumed an Hyuuga-NonHyuuga child has a chance of not have Hyuuga eyes (which would only be the case of the Hyuuga eye gene(s) were recessive).
- It could also be argued that a Hyuuga-Uchiha child will inherit one of each eye only because both are "special" eyes, whereas a Hyuuga-NonHyuuga child will have Hyuuga eyes (they're both human, therefore the children can't be called 'hybrids').
This is making me question the fate of the Senju Clan now. Did they just disperse amongst the nations and intermix with other clans?
Well, it is impossible to keep every member of a clan behind closed doors forever.