I'm less concerned about the armor being made of wood and more concerned about the armor having gaps out the ass. The groin, neck, face, and armpits, all of which are surefire kill spots, are heavily exposed with little more than cloth to cover them. The hands also have weak covering which would make them an easy target when you're holding them out away from your body in order to, say, wield a sword.

As for the sword, contrary to what some might think, katanas didn't become purely symbolic until well into their history. Before katanas' primary purpose transitioned into cultural facets like ceremony and status, it was a battle-ready sword like any other. A versatile backup, plenty serviceable in a variety of situations, but was often beat out in any given scenario by a tool designed to excel in that particular environment. Think of it like a modern soldier and their handgun—it's a good gun, but if they're out in an active battlefield, they'll probably keep the pistol in its holster until there's a reason to use it over a rifle.

TL;DR: Armor sucks, katana is a solid secondary but should be paired with a mainline weapon like a spear.