To further Ujin's point katanas weren't designed to cut through armour. Period. They are designed to VERY effectively cut unarmoured flesh, and at that they excel.
The main battlefield weapon for the japanese weren't swords at all. They were (only counting melee weapons, since the bow was the prefered weapon), yaris and naginatas (straight- and curved-bladed polearms, respectively) since they beat the swords for range, and for effect against armour.
Then as Ujin said they had coup-de-grace daggers that either were used to attack gaps in the armour, or to simply hammer point-first straight through the armour.
Swords were carried on the battlefield as ceremonial details, and as a last resort if your spear broke (which considering the durability of yaris wasn't likely to happen).
Yes, you could kill ashigaru and militia with sword since they used little to no armour, but since they had spears designed to penetrate your armour you'd prefer having a spear yourself to match their range.
Samurai armour might not be as heavy as metal plate armour, but it is very resilient to cuts, and cutting is the only thing a katana can do decently.