Both Phoenix and Palm Springs are desert cities with lots of space to build suburbs, and they both seem to have cheap land. Why did Phoenix end up growing more at a greater pace than Palm Springs, especially if Palm Springs is more popular culturally?
Although the climates are similar, the tax and real-estate development situations are radically different.
Proposition 13, a 1978 ballot measure, transformed real estate taxation in California, heavily disincentivizing new housing construction for municipalities. This was accompanied by a widespread movement for more restrictive planning, zoning, and development rules in California. These changes banned new development or greater housing density in most areas, while making new developments much more expensive in areas it was still permitted.
California's resulting housing deficit is huge, and has been growing steadily for 50 years. The housing crisis is not as bad in Palm Springs as in California's coastal cities, but the median home price in Palm Springs is still roughly $150,000 more than in Phoenix.
The resulting price and supply differential between California and states such as Arizona means moving out of state is much more attractive for cost-burdened residents of Coastal California cities than moving within state to places such as Palm Springs.
I have previously discussed some of the origins and dynamics of the housing crisis in this post.
The bottom line is that for decades the Phoenix metro area has done a better job than nearly all of California building new homes to meet demand, and home prices in Arizona reflect that.