Part of the reason is that modern-day church choirs come from the practice of using Gregorian chant in order to "pray" the psalms. This is still done today through something called the Divine Office or the Liturgy of the Hours, a practice the first Christians took directly from 1st-century Judaism and incorporated into sanctifying as well as marking the hours of the day.
All forms of Western music today is based on the Gregorian chant choral music system (the "Do-Re-Mi" note system), and our understanding of harmony is based on this form of prayer developed by monks. Choirs grew out of the choral music system, which were developed to either sing for the congregation, lead the congregation in prayer, or the like. Eventually hymn singing was assigned to them, especially after the Protestant Reformation and even for the first few decades after Vatican II in the Catholic Church (Gregorian chant has since been restored to the Catholic Church as well as found its way into most other Christian denominations).
Adapting the choir system might just "smack" too much of "Christendom" for the JWs. It would also lead to studying music theory, which could lead some to backtrack to some of this information and see where and how Western music came about, risking exposure to such things as early church history and causing a backlash effect.
This is actually part of the reason why the JWs went to great extent to avoid using other hymns from other faiths, not just because they originated from other religions, but there is significant history behind many of the hymns that could in fact counter some of the teachings of the JWs.