Oftentimes they do not as it is quite expensive to make many kinds of "grey water" safe enough to be basically touched by golfers all the time. Being in the center of the desert with high water costs, it made sense in Arizona.

Regardless, keeping that much grass alive for such a small number of people to enjoy feels like a misalignment in priories of a local water authority to me. With the general trend towards water insecurities the world over I'm a bit upset with golf courses.