Board Thread:Theories and Speculation/@comment-25319479-20171101152711/@comment-28044177-20171108093701

Sure Hashirama was the only Senju noted to have the Wood Release trait, but it's probably rare even in the Senju Clan. The Kaguya Clan had the Shikotsumyaku trait, which was noted to only a appear once every generation(with Kimimaro being the last one to have it). The Stone Village's own "Lava Release" Clan has Kurotsuchi as a user, but not her father and grandfather(who has the Dust Release trait that never past down to his descendants, then again, Kekkei Tōta might work differently biologically than Kekkei Genkai).

I suspect that the more diluted the clan gets, the less chance of them acquiring the bloodline trait. Makes sense as the Senju Clan spread apart ever since the formation of the Leaf Village. You even have the the original "Lava Release" Clan being spread over 4 villages. Meanwhile, you have the likes of the Hyūga Clan and the Uchiha Clan that go through true breeding(only breed within the clan). Which is why practically all of their members have the clan's bloodline trait(until Hinata allowed her eggs to be infiltrated by foreign Uzumaki juice, which seems to be why only one of their children naturally has the Byakugan)(But then again, it's technically alien/god juice/eggs, and both of them are distant cousins due to shared ancestor from 1000 years ago).