Can't speak to the actual edge sharpness, but the nature of the weapon doesn't really require it. Properly employed, even fairly blunt, the impact of a spearing point or axing head would be unpleasant for an armored opponent, much less an unarmored enemy. A more dull edgee is actually more useful against armor in some cases, being more likely to penetrate or crush than turn.
A longsword with no appreciable edge can cut. Adding the momentum of a polearm is that much more dangerous. The idea of being "poleaxed" to describe intense physical disruption is still fairly common usage centuries after the weapons went out of regular use in combat.
