The next day, John saw Jesus coming toward him and declared, "Here is the Lamb of God who takes away the sin of the world!"
In their commentary on John, Gail R. O'Day and Susan E. Hylen point out what I should have been able to notice on my own but didn't, that John says "sin" not "sins" of the world. They say:
As a singular noun, "sin" points to the world's collective alienation from God. "Sins" in the plural evokes a catalog of individual misdeeds and "sinful" behaviors, which is not what John is saying here. "Sin" in the singular refers to a broken relationship with God in which we all share equally, whereas "sins" in the plural can be used to point to some relationships and behaviors as more broken than others. As the Passover Lamb, Jesus liberates the world from slavery to "sin" by bringing the world into new and fresh contact with the presence of God, so that human alienation from God can end.