Yes, I agree. By watching or hearing these plays, you can infer some extra meaning. I just believe that reading them is essential.

I've watched all 4 of the great tragedies, Romeo and Juliet, Antony and Cleopatra, Julius Caesar, A Midsummer's Night Dream, Twelfth Night, Tempest and one or two more I can't remember the names. Most of them I watched in Hindi but Hamlet and Romeo and Juliet are two that I've also watched in English. While teaching in a college, I also got a chance to direct Hamlet.