One thing that makes answering a question asking about the intentions of playwrights difficult is that many important dramatic authors have left no works to us other than their plays and thus we can only guess why they wrote as they did.
Many characters in classical and Elizabethan drama have “mad scenes” – e.g. King Lear, Ophelia, Heracles, Othello, Cassandra, etc. Often these scenes are considered showcases for acting talent, offering opportunity for portrayal of a level of extreme emotional intensity and demanding a great deal of creativity in physical and vocal presence. In terms of language as well, mad scenes allow writers to experiment with unusual and distorted language and plot elements.
One factor, therefore, contributing to the popularity of portrayals of madness in drama is that its exotic nature provides an opportunity for actors and playwright to challenge the limits of their artistic creativity and audiences to experience something that is relatively rare in ordinary life.