Why did no one else in the Narutoverse inherit wood style?

[Sherlock.]

Tsunade and Nawaki aren't full Senju cause their Grandma Mito was an Uzumaki....
Apart from Hashi and Tobirama how many Senjus are mentioned in the series who could possibly inherit the wood style..??

 

[saw2097]

I have been wondering about that as well.