England under Elizabeth's rule was actually pretty peaceful. When Elizabeth's family gained power it marked the end of terrible civil wars, so Elizabethans were trying desperately to avoid other civil disputes starting that could lead to bigger wars.
Shakespeare opens Romeo and Juliet by highlighting the civil conflict that drives the play. The Montagues and Capulets are ready to fight each other at any moment, and the Prince is trying to stop the fights from getting worse. He thinks by punishing the heads of households that he can stop them from fighting more, and the audience would be with him, the fear of civil brawls exploding into something bigger would be on their minds too.
Shakespeare uses this fear to heighten the urgency of the Montague/Capulet conflict and to show how different characters participate and try to help avoid conflict, like the contrast between Benvolio and Tybalt.
