Wouldn't it be better to build into hills or even construct artificial hills over a surface structure designed to accommodate the weight, so you're not just creating a giant well that you'll struggle to keep dry?

Actually, if one's purpose building housing to handle severe weather and high temperatures there's tons of cheaper extant designs that do the trick, like just properly insulating a reinforced structure and then incorporating features that naturally cool air like towers that catch the wind and direct it down over cisterns or through cellars to cool it off even in the middle of the day.