I have moved this to the Reference Group as it seems to be a much wider and bigger question than just referring to Arts.
From my point of view, as a teacher who has been in the profession for a few years, I am absolutely amazed by the number of people who have reached adult life and positions of great responsibility (even directors, unfortunately) and who are inexplicably able to do a simple task like deliver a presentation that doesn't send everyone to sleep.
Communication skills are absolutely vital in almost every area of life, unless you are planning on locking yourself up somewhere for the next few years. Even if you are not planning on being a teacher, for example, the vast majority of jobs require good communication skills that will enable you to communicate effectively and succinctly to a wide range of people. Even being able to present yourself effectively in interview is a vital skill nowadays. Communication skills are therefore essential in today's world.