Sure, Barbershop is arranged and carefully presented. So, were the Weavers, the Copper Family,The Dubliners and every other successful singing group. One could make a good case for excluding arranged music from "folk" but we seem to be a lot more tolerant toward some groups and styles.
Certainly, we know who wrote most of the Barbershop classics. We, also, know who wrote "Silent Night", "Oh, Susanna" and "This Land is Your Land". Barbershop harmony was the DooWop of one hundred years ago. It may be formalised, today, but its roots are as humble as Old Timey.
I am glad we are having this discussion. I didn't start this thread to increase the audience for Barbershop. I am suggesting that more of us should be singing in Barbershop choruses because it's fun. I have been a soloist all my professional life and I wanted to learn how to. better, blend with other voices. Boy, what I learned. I learned about breathing, about extending vocal range, about the different voices I had. Before each rehearsal, the chorus stands on the risers and does vocal excercises, conducted by real vocal coaches. I tell you, I had been singing for my supper for thirty years before I joined The Mainliners. I am a much better singer, today, because of what I was taught. (By the way, the Sweet Adelines are just as good, or better)