I'm not entirely sure it represents conquest. Not entirely, anyway. We have phrases like "put to the sword" as a euphemism for slaughtering civilians. However, the fact that the sword and großes messer were widely used for self-defense and duelling seems to me the great distinction between the sword and other more common weapons of war. I would prefer a naginata over a katana in combat in Japan, but I would also want a katana or wakizashi as a backup. Similarly, I would want a spear or poleaxe in medieval Europe, but a longsword or arming sword would be a convenient support option. In this respect, I think the sword is analogous to the pistol. Rifles and shotguns win wars and protect pioneers, but the pistol as a backup weapon and a means of civilian self-defense reigns supreme in the public consciousness. But while pistols often signify an officer in the military, though, they haven't replaced swords as a ceremonial emblem. And while pistols are very much another weapon requiring training and expertise to use well, the allure of the sword supersedes it. The mythologized history of the medieval era probably plays a major role, but there remains something individualistic about the sidearm, and that essence is I think the key.