If you've noticed, only these extremely powerful people use Wood Release, and Yamato who is compatible with it. But only Madara, Obito, Zetsu etc. can use it, because of Hashirama. And I could think of a theory that Yamato's a Senju, because he has the same headband as Tobirama, uses water release( probably because of wood release) and wood of course, like only Hashirama, a Senju, uses. Tsunade can't use because, as you said, is only 1/4 Senju, and she's never tried, or she's just not strong enough. Not to mention that she'd need a scroll or something.