In short, because its protections and its effects are least relevant. Milling 10 cards from an opponent's library, while it will (usually) eventually lead to a game win, does nothing in and of itself; and putting an additional body into play means another creature to carry the sword, but is often seldom directly relevant. By contrast, Sword of War and Peace deals additional damage directly; Sword of Fire and Ice both deals additional damage (to a target of the attacker's choice) and draws a card; and Sword of Feast and Famine is disruptive with its discard and allows the attacker to cast spells pre-combat (during the Standard season that it dominated, for instance, a Squadron Hawk or Jace, the Mind Sculptor) and then still have their lands untapped to keep up counters on the opponent's turn.
Sword of Light and Shadow's effects are arguably worse than Sword of Body and Mind's; returning a creature to hand is arguably less useful than putting a small body into play (since mana still has to be spent on the creature) and the lifegain is as modest an effect as lifegain usually is. But this is where the other factor comes into play: both White and Black tend to have viable removal spells, on the order of Doom Blade or Oblivion Ring, and so protection from either or both makes a creature much more viable. All the other swords offer protection from either Red or Black, the classically removal-heavy colors; Sword of Body and Mind, on the other hand, only offers protection from Blue and Green, the two most removal-light colors. Bounce spells tend to be viable parts of a format only rarely, and while punching through Green monsters is often useful, SoFaF provides that same ability with better effects and a more relevant secondary protection.
Of course, all of this analysis can go out the window in other environments; in particular, Sword of Body and Mind is often regarded as the best sword for limited environments, and in particular in most cube-drafting environments. There, the mill becomes much more relevant (since often just two swings will be enough, and three virtually always will), the protections balance out somewhat, and the additional body is even more board-affecting.