I think the issue is the people, not the cars. The people of Peachtree City, GA have a large golf cart culture. And, they still have golf cart traffic jams[1], golf cart drunk drivers[2], and severe golf cart accidents [3].
They don't 'primarily' use golf carts. They still use mostly cars. I lived there for several months. Golf carts are definitely part of the culture, the city encourages them by building paths, but the vast majority still drive cars.