I suggest that you go ahead and write your paper, focusing on the occasions when a letter plays a strong part in the plot, and then worry about your thesis statement later. It would seem to me that Shakespeare had to rely on letters in some places because his characters were all so widely separated. Even Goneril and Regan were in different parts of the kingdom because their dad had given them separate domains which amounted to separate halves of England after Cordelia was disinherited. There is no other play in Shakespeare in which all the characters are so widely separated. Shakespeare shows complete disdain for Aristotle's unity of place. By contrast, Hamlet takes place in a few settings representing parts of the castle, except for the encounter with the grave digger. Maybe it is not the "Importance" but the necessity of letters that you should deal with. The letters are important just because they are the only way some characters have of communicating with others. The letters were important to Shakespeare himself.