What is the significance and roles played by Steve and Eunice as a couple

Steve and Eunice FIGHT! That's their purpose. A Streetcar named Desire is a study of couples and the time. Women were to be submissive, couples solved their own problems. The police didn't come running or often arrest anyone in regard to domestic violence calls, certainly not like today when a call means someone is going to be arrested.

Steve and Eunice give us a separate backdrop to the neighborhood, and an insight that doesn't involve the main characters. We can more easily understand the fighting and the yelling in one house when comparing it to a similar occurrence in another. We see Stanley argue with Stella..... and we see him at constant odds with Blanche. Often we think he's a jerk, but then we hear the fighting from upstairs....... and Stella's response to the fact that the police aren't called and Eunice has been seen at the bar, Stella response to that news is to lightheartedly comment that alcohol is a “more practical” cure than the police for Eunice’s woes.