Since Act III of Romeo and Juliet is the climax of the play as well as the fulfillment of the words of the Prologue that Romeo and Juliet are "star-crossed lovers" whose "misadventured piteous overthrows" effect their deaths, the play would be altered completely without this crucial act of hubris on the part of Romeo. Thus, in order for the play to be a tragedy, the tragic hero must commit a mistake that leads to his demise. And, Romeo's killing of Tybalt is such an act.
Her is how the entire chain of events would be altered by Tybalt's having lived:
Romeo's slaying of Tybalt leads to his banishment, which in turn affects Juliet's life because she cannot, then, tell her parents that she is already married to Romeo when they suggest that she marry Paris. As a result, Juliet finds herself in a tragic quandary and desperately seeks a solution from Friar Laurence. Of course, his solution that she feign death in order to cause the parents to grieve and then be so relieved when they discover she yet lives that they will forgive all things fails as Romeo does not receive his message in Mantua. So, Romeo believes the report of his manservant who has seen her grave, fearing that Juliet has died; and, in despair he takes his own life, an act that then brings about Juliet's desperate suicide.