O.C. 53:4 says that one of the requirements for a "proper" shaliach tzibbur (shat"z) is that he have a "pleasant voice". (There are other qualities included.)
53:5 states that if one cannot find all the qualities for "proper", one should choose someone who is wise and has an abundance of good deeds. Rama adds that if they find an aged ignoramus who has a pleasant voice, and the people prefer him, they should use him.
I'm uncertain if the term "pleasant voice" equates with "musical skill" meaning at the least, the ability to sing on tune.
In much of Europe, esp. Vienna, they trained chazzanim in musical ability. Many of these "professional" chazzanim immigrated to the U.S., and many shuls specifically hired such chazzanim. This practice was quite common in U.S. shuls until about approximately 30 years ago, when it rapidly declined.
Considering that O.C. does not specifically mention that the shaliach tzibbur needs to be a "musical maestro", what was the main motive for training chazzanim to incorporate musical talent and for shuls to seek out this quality in a shaliach tzibbur? Was its motive to get the congregation more involved in joining in the prayers (which seems to contradict the true meaning of a "shaliach" which implies that he is appointed as your "messenger") or motivated by a career choice so that such people would be more likely to be hired by a shul?