While Link may not actually be a knight, he does take up the role of the "Hero" or "Knight". Even Zelda staff has called him as such:
"The games feature Zelda, the heroine, and Link, the knight." -Naoki Mori, Cinema Scene Director
So, Link might not actually be an employed knight, but his character is portrayed as the knight character of the individual stories.The whole sword 'n' shield design that Link has been given over the years is a style that is almost always used when depicting a hero or knight (in medieval settings, anyway), even in other stories and games. The sword and shield are part of what represents his character as a whole. The sword depicts strength while a shield would depict protection, and that's what he does- fights and protects. Removing the shield from his design would probably throw off his character quite a bit. Even when he had the Biggoron Sword in OoT, his shield was still present. Fierce Deity lacked a shield, and his characteristics seemed to have vast differences compared to the true Link.
While dual swords might look cool on some characters, they don't fit them all. For example, Lloyd Irving of Tales of Symphonia wielded dual swords, but he lacked the ability to protect himself and others... at first anyway. The lack of a shield fit his character nicely compared to the enemy, Kratos, who wielded a buckler of sorts. Kratos took the role of the Chosen's body guard. Being that he was a protector, the shield fit the role.
So now you can probably see why having a shield fits Link's character archetype better than dual swords would. I'm not saying Link wouldn't look neat with them, but I hardly see it fitting the role he's so often given. Now, if they decide to go ahead and make that drastic change they were talking about years ago, maybe they'll change Link's demeaner, and in that case, perhaps dual swords might work. But for now? I'd rather not see it.