Customer focused is another thing not very much associated with career progress.
Think about who is pushing the growth and the expansion of the business you are part of?
Those are, of course, the customers. Depending on your position in the company, you might have more customer exposure or not at all.
What are the benefits of having a good relationship with people in general? Potential customer might what you to join their team and boost your career.
Good relationship with your customer might also show to the senior managers in the company how talented you are. It is one thing if you scream how talented you are, and another if other people recognize you as a talented person.
Another good thing is, you practice this valuable skills that are transferrable no matter what your job is.