Indeed
Once upon a time, I was a desktop technician on an inhouse team. After years of doing it well, they decided to promote us to different positions, and bring in a team of young guns with our hardware vendor to do the job cheaper.
I went on to manage projects, but within six months I had a new responsibility. Teaching the young guns how to provide good customer service. I heard all the complaints from the customers, many of whom had known me for years. I worked with the team's supervisor to improve their communications and skills. I even sat in on interviews when they hired new techs.
Mad tech skills are only part of the equation.