I'm an architect / urban planner who used to live in Phoenix (Tempe, actually). There's absolutely no reason a city in that kind of environment can't be walkable, even in the height of summer. There are two key components:

First, you don't just need mixed-use, but density of mixed-use. This is why London, where I now live, is walkable. There's a good cafe within 2 minutes of my doorstep. A doctor's office and a grocery store and a bakery within 3 minutes. A park and a pub and several more shops within 4 minutes. A hardware store within 5 minutes. I very rarely am required to walk for as long as 10 minutes. Even in an environment like Phoenix, these distances would be perfectly walkable. I've also spent time in Reykjavik in January, and found it quite walkable for exactly the same reason. This has nothing at all to do with climate.

Second, what does have to do with climate is shade. Currently, cities like Phoenix are actually much hotter than the surrounding desert, due to the "urban heat island" effect. This is primarily driven by the abundance of asphalt and other high-thermal-mass, low-albedo surfaces. But cities don't need to be designed this way. If you look at traditional Middle eastern urban design, you can find cities that actually create "urban cool islands", and are (relatively) livable without air conditioning. Key components of these techniques are:

- Very narrow roads / alleys, such that buildings are continuously shading each other and sunlight doesn't reach the ground

- roofs painted white to reflect the sunlight & heat back into space

- "cold sinks" to capture cool night air

- Wind catchers and various other devices to funnel prevailing winds into the alleyways, and to convert thermal updrafts into air movement even when there aren't winds, creating siphons to circulate air out of the cold sinks

- courtyards with pools and vegetation to create evaporative cooling from the moving air.

These techniques and others have been well-understood for several thousand years. They're detailed in a lovely book by Egyptian architect Hassan Fathy, called "Natural Energy and Vernacular Architecture". Highly recommended.

However, all of the above is incompatible with low-density development and streets that can carry large amounts of vehicles. The former precludes the necessary density of services, and the latter precludes any of the environmental adaptations that are necessary to make the desert livable. But these are man-made planning choices, not dictates of the environment. Those choices can be un-made.