Act 4, scenes 1-3. Why don't Romeo and Juliet leave Verona as a solution to their problem?
Following his exile, Romeo says:
There is no world without Verona walls,
But purgatory, torture, hell itself.
Hence-banished is banish'd from the world,
And world's exile is death: then banished,
Is death mis-term'd: calling death banishment,
Thou cutt'st my head off with a golden axe, And smilest upon the stroke that murders me.
Verona was, more or less, a city-state in 13th C. Europe, so to leave it was to immigrate to another country. Exile was death. Families clung together for support. There was no chance to lead an independent life otherwise. One could become a monk or join a nunnery, but neither take in married couples.
Romeo and Juliet are kids; they are bound to their parents. To move out of their protection would mean begging for food and shelter. And they are privileged. As only children, they live like royalty. What jobs, what status, what dowry, what land, what rights would they have outside Verona's walls? None. One's name and reputation guaranteed prosperity for generations to come.
Lord Capulet says of Romeo:
Romeo's got it made, even if he is secretly married to his enemy's daughter. When Romeo is banished, Lady Montague kills herself, such is the effect of his exile. Lord Montague says:
A secret marriage is one thing, but a secret identity outside the city-state is another. It is better to marry a mortal enemy than to exile. It is better to suicide than to exile. Italian families are tight, to say the least.
In the William Shakespeare play, Romeo and Juliet the young lovers didn't leave Verona because it wouldn't have worked. We saw earlier in the play how Capulet reacted to Juliet's disobedience. His reaction would have been much stronger if Juliet bailed out of an arranged marriage. As an influential man in Verona, this would have proved quite embarrassing for Capulet. In edition, there is no doubt that Paris had paid an acceptable dowry for the promise of Juliet's hand and joining his name with an influential family like the Capulets.
So the only solution was one where the parents would have to accept the inevitable. Thus the friar concocted the scheme of arranging Juliet's "death." Faking her death set up a chain of events in which she and Romeo could have left Verona and lived undisturbed by Capulet.