Sean — Nearly all "desert" courses in Arizona use reclaimed water, which otherwise would be displaced on the open terrain and allowed to move downstream to the Colorado River without decent filtration. Using a field of 70-90 acres of turf as a filtration allows the recycled water to move back into the ground from where it originally came. This is good science — and very good environmental practice. Even when desert courses may use potable water, it is typically blended with some form of gray water.
Golf courses "borrow" water. They really do not "use" that much when you delve into where the water goes.
There are a few factors that drive desert courses not getting better "love" from raters and the hoity-toity purists:
1 - A lot of purists take their roots from the East Coast of the US or across the pond...no deserts, so fair to imagine a desert setting as being unfamiliar
2 - Most all desert courses are modern...and, like the movement INLAND back in the late 1700s and early 1800s, it took a long while to appreciate INLAND settings as opposed to the coastal/links locations (maybe we will never appreciate desert settings)
3 - As follow up to #2, "old be better" when it comes to golf love, and even in the modern "loved" courses we see them taking on the look (95% of the time) to "old" versions of the game...not all that possible with desert courses because there are no "old" versions to appreciate (Desert Forest being one exception...but, still only c. 1960s)
4 - Housing, as Tom D points out, is prevalent on desert layouts...and there are few trees to conceal them, unlike — say — Muirfield Village or Cypress, where housing sits back in the woods even though it is within a few hundred feet of some fairways
5 - My first project was basically a par-3 course masquerading as a regulation...I had way less turf than needed, because my instinct was to preserve the rock formations and land forms...that did not work all that well, but over the years we have made it better...I think Tom D's idea for more par-3 desert courses is spot on!