The world Tolkien created is a profoundly pluralist one. The "good guys" are consistently shown to be inclusive of many cultures and ideas (the most famous example being the Fellowship, with members drawn from all over Middle Earth), while the "bad guys" are consistently shown to be focused on exclusion, domination, and the control of the many by one.
This is even more clearly shown through the characters tempted to switch sides: Thorin's mistrust of anyone beyond his own kin is part of his "madness" and doom, and the visions of power given by the Ring always involve the domination of those who would oppose the wearer. Even Sam, who envisions the ability to create great huge sweeping gardens (seemingly a beautiful act of creation), is being tempted toward a path of wiping out whatever is in his path in order to make everything the same.
The Tolkien scholars in the LOTR:EE documentaries discuss this: Sauron's doctrine is a kind of obsessive monism. One eye, One lord, One ring to rule them all. He brooks no disagreement, allows for no other perspective. Meanwhile, the Free Peoples of Earth have, between them, nineteen rings and countless leaders and factions. Even the spiritual side of Middle-Earth, while nominally monotheistic because Eru-Iluvatar rules above all, is absolutely brimming with Ainur and Valar and Maiar and nature spirits, and the creation of the world involved music created by all the Ainur together, not simply Eru on his own.
Following this philosophy, it makes sense that Melkor would be a single figure at the top of his "evil empire", without a partner or companion. The whole philosophy of evil in Arda is that of control and domination, and as Gandalf says in the FOTR film, the Dark Lord "does not share power."
pictured: Diverse people working together
pictured: Not so much