I'll say upfront that I am not a nurse, but I can also say that interpersonal skills are critical in any profession in which you interact with other people. This is especially true in professions where your "customers" are in stressful situations and don't feel comfortable or knowledgeable. We run a 24-hour emergency center and interpersonal skills are one of the key traits we look for when recruiting staff and medical personnel.
Susan and Suzanne have explained really well how good interpersonal skills can help you be a better nursing professional.
I once read the following article that said "Decades-old studies have shown that primary care physicians sued less often are those more likely to spend time educating patients about their care, more likely to use humor and laugh with their patients and more likely to try to get their patients to talk and express their opinions."
Have a great career!