On, I dunno. I can think of a two-word answer that might have had a bigger impact on Tucson than a mere war: air conditioning. Prior to widespread a/c, much of the South and Southwest was nearly uninhabitable, at least for commercial purposes. Population of Pima County, Arizona, in 1940: about 73,000. Now: about 975,000.
Spot on. Ditto Florida
Interestingly enough, some of the first places in the US Southwest to get mechanical air conditioning were hotels used by railroad crews in Arizona, especially in Yuma, Phoenix and Tucson. These replaced the little huts that were cooled by evaporative cooling, essentially running water through the outside metal wall of the house so the whole building cools by Peltier effect.
A/C don't work worth spit when the humidity is in the single digits.
You had dry heat. How do you think New Yorkers did it in their skyscrapers back then in soppy humid weather ... wihtout AC?
Now for me, I know WWII had an impact on L.A.