There are plenty of things less sustainable than golf in the desert. Firstly, golf BORROWS its water, about 2% of Arizona’s total usage. And it is correct, most courses use recycled water in the populous cities. Streams, as Gib notes, are recirculating systems. They only lose via evaporation. Most are there to aerate stored water volumes.
Going forward the trends will be less water (a mainstay of any arid climate work), turf reduction, turf innovations (new varieties) and water transfers. Example: Seawater extractions pumped to Arizona and California where it gets BORROWED and eventually returns to the ground, air and ocean.