Many things in Yume Nikki are monochromatic. What this represents, like much of the rest of the game, is up to interpretation.
Fan Speculation Edit
One possible interpretation for the monochrome scheme is that is symbolizes past events, much like how we use greyscale to symbolize something in the past nowadays. The occasional red bits found in these black-and-white areas are meant to draw attention to a certain thing.
The White Desert's monochrome design has been suggested in some theories as a representation of past events in Madotsuki's life. In these theories, Monoko and Monoe are typically seen as siblings Madotsuki knew before shutting herself off from the world. Monoko is argued to be a girl who was injured or killed in a car crash, represented by her body having bones out of her body (among other injuries) appearing when the Stoplight Effect is used. Monoe doesn't react in the same way as her sister, instead disappearing when talked to. This could represent a parting between her and Madotsuki following the event, with the smirk on her face indicating she felt no remorse for her sister.
The prolific images of body horrors in the White Desert evidence memories of Madotsuki's violent past.