Are you sure? Died in the war doesn’t necessarily mean killed by a fodder. Let look at 3rd Raikage. He died taking on an army by himself. May have been a similar deal with Hashi. Or maybe he gave his life to save others? Somethings like that.
One arm cut off, thus no Mokuton, so he isn't so powerful anymore. He gets ambushed. He can't use Mokuton or Suiton/Doton cause he can't form hand-seals singe-handedly. Thus he dies.
Hashi died because of overusing shinsuusenju and creating the chakra nature determining trees.
Using litmus papers grown from a tree that absorbs chakra, Kakashi gives them to Naruto.
Hashirama got the 5 nature releases from mokuton statue , which absorbs his lifeforce, leading to his death in the era of peace, when he was constructing the litmus chakra trees in konoha.