*eyeroll*

Do a quick search of Red Mage in google images and tell me how many swords you see compared to other weapons.

Red Mage, without a doubt, is a Iconic Sword job. They're entire imagery is based off of Spanish and French fencers and musketeers.

Yes, mechanically, they could equip a great variety of weapons, that's due to being a jack of all trades type. But as an Icon? Sword, specifically the fencing styles.