Kenjutsu - The Art of the Sword② 

This philosophy was applied in a peaceful time like the edo period, jin sakai was in kamakura period it was still feudal japan and it was the mongol invasion so it was a time of war.

Totally true: The spear (yari), halberd (nagina-to), and bow (yumi) were the dominant weapons on the battlefield. The "Uchigatana" (single-sided edge) fulfilled the function of a secondary weapon. On many occasions, it was not even used, since many encounters ended on the ground, the knife (tanto) ended up being the weapon of choice for fighting melee due to its speed and versatility, reaching the vulnerable spots of the armor easily. The katana only became relevant in the Edo era, when there were no longer wars with extensive armies, armor was no longer necessary and skirmishes occurred mainly in streets or alleys where long weapons did not work. This was the golden age of the katana and wakizashi use and many schools emerged or the ones already in existence specialized it's efforts in this new way of fighting. For this reason, when you see a demonstration of these old schools, what is most observed is their huge repertoire in the technique of the katana / wakizashi over halberd and spear.

Horse + yari = death

Well yes, but during the eco period the katana was a good weapon because people were always trying to ambush and assassinate you, that was when iaido was made because if you could draw your sword fast while someone was attacking you, you would win the fight