There are a few reasons to use more than one antagonist in a story.
For one thing, especially with regard to the superhero film genre, traditionally, there is a lot of focus on their origins and backstory, which very often leads to a deficiency in the attention given to the main character's arc. Consider for example that in the first four Batman films, the villains probably had more total screentime than Batman himself, and the stories were in large part driven by the villains' tales.
Contrast that with the two Nolan films, in which we really got no origin stories for the main villains, no origin for the mobsters and smaller bad guys, and no origin for one of the two larger supporting villains (Scarecrow and Two-Face). Only Dent, who became Two-Face, got a significant "before" story, and it was a character arc that drove the overall narrative of Bruce/Batman's own arc.
Nolan's films have put a great deal of attention on using every story element and other characters' arcs not only for their own specific individual purposes and arcs, but to feed the larger overarching story and characterization of Bruce/Batman. Dent's "white knight" story and tragedy of downfall was its own story, but ultimately was a subplot of Bruce/Batman's "dark knight" story. Dent had to die a (false) hero, so Batman could be a true hero who lives to see himself become the villain. Always the stories and arcs are in service to the main character.
Another thing to consider is the length of the films has increased, with "The Dark Knight" for example being about 30 minutes longer than any of the first four films, and "Batman Begins" being about a quarter of an hour or so longer. The added time, plus the fact that Nolan's films avoid extensive origins for the villains that would use up a great deal of time and focus, means there is far more time and attention revolving around the main story and Bruce/Batman's arc. Fifteen minutes of extra time, for the sake of comparison, is about how much total time Scarecrow/Dr. Crane was on the screen in "Batman Begins."
In addition, the arcs in the new films are driven by the questions Bruce has to face (every conflict in film can be identified as a question, such as "will Rocky dig deep to find the champion in his heart and win the championship?" or "can Bruce overcome his fears and become a symbol of hope, while saving Gotham from those who would plunge it into fear and hopelessness?"). So instead of relying on one villain to represent one dilemma/question and its secondary layers, the films explore many different and typically conflicting dilemmas/questions and their multiple layers. The films explore more complex elements of Bruce/Batman's choices and decisions, and the impact they have on his world. There's a lot more subtext when you use different elements and villains and situations to constantly comment on and drive forward Bruce/Batman's characterization and actions.
Lastly, there is undeniably the simple element of "increasing the threat level" that is served by using multiple villains. This allows the writers to avoid having to make any one single villain too powerful, which could (and often does) lead into far too fantastical events and plots by the villains, or conversely leads to the threat not being big enough and so you might feel "why did it take Batman so long to take this guy out?" More villains mean more different threats from different directions.
Now, in three of the first four Batman films, they used several villains, and it was primarily (in my opinion) motivated by (a) upping the threat level, under the thinking that "if one villain is good, then two must be better, and three must really be the best," as they say; and (b) a tendency to put more emphasis on Batman's villains as the more interesting parts of the story, and thus a need to spend more time on the villains with origin tales and multiple villains. There's the added point that they like to cast big name stars in the villain roles in the first films as well, so they gave them lots of screen time and attention for that reason as well. This all added up to films that had more time for the villains than Batman, which was done intentionally.
So there are different reasons that the original four films and the most recent series of films have all used more than one villain most of the time.More questions on Batman: