Thats a huge amount of constant power and infrastructure, which is just not going to be built.
Easier to build an underground city with high ceilings and taking advantage of physics than managing to give AC to everyone in the region, which is to say both options are extremely difficult and require pre-existing infrastructure.
And this still doesn't solve the problem of what precisely people will do for work in the region
Ancient Iranian architecture was quite close to that, which you may be alluding to: http://www.cais-soas.com/CAIS/Architecture/wind.htm
What people will do? Well, same as everywhere else, everything from agriculture to software. It's more a question of how many of them the local agriculture can support. The number of people who've fled Syria is more than its entire population was in 1950. Similar applies to places like Yemen. Malthusianism may not apply globally, but it can certainly bite locally.
no wonder persians were called 'educated arabs' in the past.
We would have to create infrastructure for AC-based indoor living in the entire region and beyond on a grand scale, or only for some and see the rest of the population live in a vegetative state during much of the year. If climate change and the predictions are real anything less is futile. Basically, the entire region is becoming Arizona - without AC for most people, much higher humidity directly at the Gulf, with even less freshwater and many more people who also are much poorer.
Just a dark thought: Maybe there simply is no solution. The climate problem is independent of all the human problems, so solving them, already seemingly impossible, would not even help much with this new issue growing stronger.