:flaw:
Im going to have to stop you right there. You are seriously overrating hashirama and underrating nagato.
first of all you are assuming that in this situation Hashirama knows all of Nagato's abilities. Hashirama did not live in an era with a rinnegan because it has never been stated that hashirama met madara post fight at the valley of the end. Hashirama would fall to the same disadvantage that jiraiya did. not knowing how the six paths worked. Plus you are pitting hashirama against each path one at a time which is also flawed because nagato used teamwork when fighting with the paths. Hashirama trying to use mokuton against all of them at once in a strategic manner would result in being attacked by at least one. now that, that discusion is out of the way. let me prove you wrong one path at a time.
Animal path: The cerberus has been shown to escape easily from things such as bindings and traps. the cerberus is not only physicly strong enough to break out of traps that cannot be escaped from, but also can divide to break out of it's traps. The other summons are also strong enough to break out of metal and break through concrete, if that is true then they can escape from wood. Also the bird is capable of ...FLYING! ie: can't be contained by mokuton because it would just fly out of the way.
also the animal path can summon the other pains. as soon as one pain is caught by mukoton the animal pain can simply summon them to another location, including one of Hashirama's blind spots.
preta path: no, it's abilities are not automatic. However you again forget how fast it is to turn on. Jiraiya flew at him full speed with the rasengan and the preta path almost instantly started absorbing it. You also forget about shared sight. even if hashirama got to a spot where preta wouldnt see the mokuton, the other pains probably would and preta would begin absorbing chakra.
also if preta was caught in the mokuton he would simply start absorbing chakra by contact and the wood would be defeated.
Asura path: yes, Hashirama can use medical ninjutsu, however we do not know the extent of it's abilities (speed efectivness, ect) Not to mention that Asura has been shown to be so incredibly strong that he was able to rip off jiraiya's arm and crush his throat in one swift motion. Asura is incredibly strong and fast so mokuton would have difficulty in grabbing him and holding him down. Even if the mokuton got a hold of him he could simply use his bladed tail, missiles, or energy cannon to smash the mokuton.
Human path: you are partially correct on this note, that human path's abilities are avoidable, however it is rare to use human path as a full on fighter. Human is more of a supplimentary fighter rather then a full on fighter. Human path would be waiting behind the others. waiting for one of the other pains to grab hold of Hashirama. if asura or preta grabs hold of hashirama then his mokuton would most certainly be out of the question (his chakra would be eaten up so no ninjutsu/ hold his arms so he cant make handsigns) Then it would be a rather simple matter of soul removal.
Naraka path: This one you are not only ignoring the naraka's abilities, but you are also completely incorrect. Naraka and Human have nothing to do with each other and can function perfectly without each other. Naraka is again, a supplimentary fighter. hiding in the back ranks and probably would be well guarded. naraka would revive any pains that are somehow defeated and would be protected by deva at all times.
Deva: This one you were almost insulting Deva and contridicted yourself. Shinra tensei has been shown to be powerful enough to smash rock, deflect bijuu dama, and level all of Konoha. It could easily break trees. Even if the mokuton were strong enough to prevent Hashirama from being pushed, that is a double edged sword. Shinra tensei has been shown to be able to smash bones just from impact force. If Hashirama held himself down with mokuton that would only be making him stiff to the impact instead of free moving.
here is an example:
Would you rather be standing on railroad tracks and be hit by a train, or standing against a wall and using the wall to support yourself and then getting hit by the train. Using the wall to support yourself you are only turning what would have been a life threatening blow from the front, into a body crushing double impact. You would be crushed to death.
the same applies to hashirama supporting himself with mokuton while being hit by shinra tensei. The impact would probably do near fatal damage.
Again you ignore teamwork. By using bansho tenin, deva can draw hashirama into the arms of asura, preta, or human path, all of which would leave him in a fatal situation.
The chibaku tensei is one of the few points I will agree with you on. Hashirama probably would be able to destroy it with mokuton. However considering the above, i doubt it would be necesarry
-The gedo mazo: The strongest that the shinobi army could muster couldnt even hinder the gedo mazo. Insinuating that mokuton would be enough to stop a giant monster empowered by several tailed beasts is a massive flaw on your part.
other points to note: You seem to forget the chakra disruption blades. not only are they capable of cutting through chakra and flesh wih ease, they could cut through mokuton. Once pain gets one blade into hashirama, then he can start manipulating him and holding him down. Even one blade is enough to alter motions and hinder the opponent, resulting in the other pains being able to overwealm him.
Yes Hashirama is a great shinobi. but come back with more solid answers then mokuton, mokuton, mokuton. when you come up with a better solution. tell me.