There's sharp enough, and then there's massive enough. You do CLEAVE through mail and plate with massive enough weapons... that's what claymores and zweihanders were made for, after all. You DO cut through lesser armors, provided the armors are fabric/hide/fiber based, and provided the blades are sharp enough. BUT more importantly is the skill with which the weapons are wielded. Even if the sword is massive enough to collapse several fully plate armored knights with a single swing, all Guts style, good luck having the physical strength, proper posture, timing to set up, and space to make a full arc to ACCOMPLISH such a damaging blow. Less cumbersome weapons were designed with the specific intent of breaking heavier armors, like flanged maces and war hammers, but it's a popular romanticizing of weaponry to just think about the swords, the swords, the swords. As mentioned above, spears and polearms and arrows were used specifically because they were so much more effective at this task, and it didn't take a superhuman to wield them.
But armor CAN be cut/sliced through. Just, like I said, it's not metal armor that's gonna be getting cut. A sharp enough sword, with the right shape, and the right force applied at the right angle, and it will slice through many layers of leather like a hot knife through butter. This is what the katana was used for. It was a very fragile blade, it wasn't designed with piercing in mind, but with drawn slicing. Proper kendo (the art of the blade) teaches withdrawing the blade as you swing it, to create a slicing movement that better utilizes the blade's razor sharpness, rather than a chopping downward stroke. The slicing, focusing all that energy on an INCREDIBLY small surface area (the edge of the sword) goes through light armors like nobody's business. And most samurai and warriors of feudal Japan (Hell, fairly recent Japan, even, because it went through VERY different modernizing than the West) wore something not too dissimilar to brigantine armor; layered leather. These were excellent against piercing weaponry, but very susceptible to the slicing weapons used by samurai.
But, you're not placing archers who wear lighter armors instead of plate in these Western-centric battles out on the front lines for them to be faced with warriors wielding gigantic exacto knives. Medieval warfare in the West focused on heavy armors and shields, and weapons designed to get past those. Not sharp weapons that were made to cut through softer armors.