I agree with the premise of your question, and here is why: nearly everything in life, including business and personal life, is based on relationships. Imagine a doctor who does not listen to his patient, a business owner who fails to communicate with his employees, or a couple who never communicates. The results would be disastrous. The key to every successful relationship is, of course, communication.
Listening, a vital component of communication, is necessary to develop and maintain successful relationships. It is by listening that we learn information and demonstrate empathy; those who stop talking so much and begin to listen are necessarily going to discover things they did not know but will be invaluable in the relationship. Consider a doctor who takes the time to listen to all his patients' symptoms and is able to make a more accurate diagnosis; or a business owner who listens to his customer feedback and makes improvements which enhance his business--and profits.
Listening is a critical part of communication, and poor listening can contribute to a host of interpersonal and organizational problems.
Being a good listener is a skill which will reap plenty of benefits for those who master it.
Effective written communication is another essential element of communication. Because written work is representative of the writer, it is imperative that written work (e-mails, resumes, documents, reports, and more) be accurate and express the precise meaning the writer intended. Poor grammar, careless wording, and inattention to detail in written work "speak" quite loudly to those who read it. Conversely, written work which is concise demonstrates respect for the reader's time, and written work which is correct demonstrates professionalism in the writer and ultimately greater success.
Speaking is the most obvious form of communication, so most of us tend to think we have mastered it; while that may be true in some ways, there are many aspects of spoken communication which can either move us forward or keep us from advancing. We all have more and less formal speaking vocabularies, and certainly knowing one's audience is crucial to being a successful verbal communicator.
Other factors in this area include non-verbal communication ("speaking" which is done by the attitude and stance of the body); eye contact (a significant factor in interviews, among other things); tone of voice (which can "say" much more than the actual words we speak); and interrupting (which indicates a selfish communicator who is more concerned about what he wants to say next than in listening to the speaker). Each of these rather "silent" communicators is sure to impact the speaker's success and failure in all kinds of relationships.
In short, effective communicators are more likely to have successful relationships, and successful relationships generally lead to success in other areas.