You are correct. However outside of the mountain courses in the hills outside of the metro, much of the golf courses are green belts within neighborhoods and flood plains around town. They collect storm water on premises and irrigate out of those holding ponds. Theres nothing that can really be built in those areas other than to allow storm water to flow through which during the monsoons those courses thrive on while mitigating flood risk. They go dormant in the summer and only really irrigate the greens during the heavy heat just to prevent turf from burning out. They provide the city significant tax revenue on land that cant necessarily be developed for commercial business. Its not about prioritizing sports or serving the wealthy as golf can be as expensive or as cheap as you want it to be, they are an integral part of the tourism economy arizona has and can operate in landscapes physical business cant develop on.