More to the point, nearly all of that growth has taken place in an
air-conditioned world. Urbanization of the U.S. South really only took off once the air-conditioner became mainstream.
Those other cities have a population that is adjusted to the heat - they grew up with it, their ancestors grew up with it, they're genetically and culturally adjusted to the climate. By contrast, the U.S. South includes a large number of immigrants who are only there because air conditioning exists. It's a mystery why anyone would want to walk around in 100 degree heat with 90% humidity, because they certainly wouldn't.