Iran's ancient AC system

This diagram is wrong, it simply wouldn’t work if that was the design. There is no Venturi effect suction power to draw in the cool air.

The wiki has a much better diagram that actually would work ; https://en.m.wikipedia.org/wiki/Qanat#/media/File%3AQanat_wind_tower.svg

Qanat wiki:

https://en.m.wikipedia.org/wiki/Qanat

And the concept is still in common use. The modern evaporative coolers are called "swamp coolers" in the US.