I think at least partly because of the symbolism of them that most westerners will have picked up almost by osmosis. Swords of old had power, they had names, they had a spiritual heft behind them. Think Excaliber, Hrunting (Beowulf's sword), Joyuese (Charlemagne's). It's similar in some respects elsewhere too -- many Samurai named their swords, and a thing with a name....
Thanks to all that mythology etc, swords have a special weight in our heads (or can do depending on how you play it). Anduril, Narsil, Glamdring, Guthwine..,
The sword is symbolic of justice, of chivalry, of oaths made and kept.
It's only natural that should bleed through as we write, and as we play on those mythologies.