One reason that the opening scene of the play is set in a public square is in order to emphasize the public dimensions or consequences of private behavior. The feud between the Montagues and the Capulets is not simply a dispute between two private families; it is a conflict between two wealthy, influential, and socially important clans, and it thus has serious consequences for Verona as a whole. It affects not simply the members of the genetic families themselves but their entire bands of retainers, followers, and allies. Shakespeare shows how disorder at the individual level can quickly infect and disrupt an entire society; chaos at the level of the microcosm can disrupt the macrocosm as well. In a society in which important families were very important indeed, quarrels within or between those families had profound consequences for the society as a whole. This important point would not have been emphasized nearly so clearly if the opening scene had been set, say, within a private home.
This scene primarily sets up the conflict between the two houses and it shows the impact that the feud between the families has on the city at large.
First, this scene illustrates the intense hatred that the families have for each other; even their servants become involved in the fray!
Second, the Prince is able to break up the fight and establish a few ground rules
- this is NOT the first time this has happened--this is the THIRD time the families have started fighting in public, and both he and the rest of the residents have had enough
- this allows the Prince to lay down the "new and improved rules"--if there is fighting in the streets, whoever participates shall be put to death.
This, of course, comes into play in a later scene where fighting in the streets again occurs.
You could say that this is necessary for a variety of reasons. Here are some:
- It would be illogical for the servants of the two families to be meeting each other somewhere that wasn't in public. It doesn't seem likely that they'd go over to each other's houses to fight in private.
- It is useful to be out in public so that the Prince can intervene. It's important for the story because the Prince pretty much tells them all to knock it off or else. So later on in the play when Romeo kills Tybalt, he gets exiled because the Prince is angry. This sort of sets the stage for that.