EQ becomes more important the higher up one goes in an organization.
When you first join a company, they usually look at your CV, photo and credentials and then opt to call you for an interview to verify if those credentials plus your attitude meets the criteria they are looking for and then you join them at the frontline.
When you start performing and then get promoted, you begin to do less of what you first came in to do and begin to supervise others to do what you were mainly doing but still continue to do some of the work and take on other more difficult tasks.
When you are more senior and experienced, you get promoted to management and now your role is to mainly motivate, inspire, lead, mentor, give feedback, share stories and create an atmosphere of comfort and learning. This requires a totally different set of skills. Much of the skills you need are EQ related.