For a long time many things about the Mokuton really irked me, so now I present my own two cents about how Hashirama's famous power.
Recap and some insightful thoughts:
Until the latest chapters we were led to believe the origin of the Mokuton was Hashirama Senju, the first Hokage. Yamato, Danzo and Madara had his DNA implanted and were thus able to use it, Zetsu was created from his very DNA and lastly Obito was partially merged with a Zetsu.
Though now we know better, Zetsu's are far older than we were led to believe. Those artificial beings were created by Kaguya using the remnants of the god tree and the very people she enslaved. So one can assume that they are a hybrid, half plant and half human.
Now with this revelation it is at least very easy to understand how the Mokuton is able to subdue tailed beasts. The Mokuton like the Sharingan is a derivation of the original power of the Shinju.
So how Hashirama got the Mokuton?
The Mokuton is not a hereditary power of the Senju
There was never any real indication that the Mokuton is something that belongs to the Senju Clan, it's not the counterpart of the Sharingan. No descendant of Hashirama ever had it, only those who had his very DNA injected into themselves were able to manifest it.
The Mokuton is not a power gained through being the reincarnation of Ashura
Naruto the only other transmogrification of Ashura we know had never shown even the slightest hint that he could manifest the Mokuton. Also Ashura himself was born without any hereditary power if we can believe what the Sage told. This brings up the question why should Ashura choose a "vessel" which has a bloodline bestowed upon itself, wouldn't that contradict the whole story of being the "underdog"?
The fate of the sons reborn?
Hagoromo's sons fought against each other, much like Hashirama and Madara or Naruto and Sasuke. But there is a difference. The sons destroyed each other during their war, Madara was killed (and sort of resurrected himself) by Hashirama and lastly if we can believe Naruto's prediction a fight between him and Sasuke would kill them both.
So the first of my assumptions is that the sons reborn are fated to fight and kill each other, this is the circle that needs to be broken. You may think I got something wrong, because Hashirama against Madara didn't end that way, but that is exactly a part of my theory.
Why is Hashirama special?
Because someone gave him the power of the Mokuton, something he was not meant to have.
It's not hard to guess who was responsible, because there was only one player at that time that had the power to do exactly that, Black Zetsu. He was the one who had the resources to bestow the power of the god tree upon Hashirama. But what was his reason?
Black Zetsu was the one who helped to create the Curse of Hatred that shrouded the Uchiha. The reasons for that are fairly simple, to reawaken Kaguya he needed someone with the Rinnegan. Only a reincarnation of Indra could do so and only when he united his chakra with that of a reborn Ashura. So Black Zetsu instigated this all to ensure the next Indra and Ashura would fight each other, that was his reason to plunge a whole clan into darkness.
Although it did never work, there was never a Rinnegan before Madara. And the reason for that is simple, the transmogrifications killed each other as it was fated.
So Black Zetsu took a gamble, he tipped of the balance of power and inserted a part of the god tree's power into Hashirama giving him an advantage in the fated fight.
Being a descendent of the Sage and Kaguya allowed the integration of this power into Hashirama. This furthermore easily explains why nobody else ever showed the Mokuton, because it never was inside Hashirama's or the Senju genes.
