These are fair points. To add on:

Swords were fairly common weapons. Polearms were preferred battlefield weapons, but swords were convenient to wear for daily life. In Japan, only the warrior class had the right to wear two swords -- and later, they were the only ones allowed to go armed at all. Their prevalence ingrained them in popular consciousness.

Despite their commonality, mastering the sword still requires immense dedication. Skill in swordsmanship reflects a great investment of time, energy and resources, as well as discipline and mindset.

Legendary weapons do lend a supernatural air to the sword. On the other hand, in at least some cases, the wielders had to earn the right to carry the sword -- or the sword itself was a reflection of the man. By pulling the Excalibur from the stone, Arthur signified that he was the rightful king of England. Other swords in the link you put up gained honour and fame because they were wielded by famous people, and were associated with great deeds or myth.

The staged duel certainly makes for a visual spectacle. And that alone can explain a long-standing interest in swords in visual media. But it takes skilled wielders to make the duel look interesting.

The thrust of this article is to go beyond mere spectacle and visual appearances, and deep into the realm of myth and archetype. The sword in itself has no will of its own, only that of the hand that wills it. And the swordsman reflects the archetypal masculine conqueror across the ages.