The petro-dollar-rich desert nations have a bigger problem...
...than just water.
Their mere existence at the scale that they exist today is very, very expensive. The long-term solutions to their problems are even more expensive. The only reason that these populations get to exist at anything beyond a 7th-century standard of living, much less their their current scale is due to the income provided by world-wide oil consumption.
What is going to happen when the rest of the world finally frees itself from the "addiction to oil"? What are these people going to do then?