Not all of Arizona has dry, blowing dust. Only parts have haboobs, and they are nasty. Other parts only get little "dust devils" from time to time when the winds are right. Wildfire season is probably more threatening in parts than the dust. There are quite a lot of evergreen trees in Arizona despite it being desert. They don't do too bad, but when they get too dry of course it is a fire hazard and when they catch on fire...don't want that tree and its' pine cones going boom.
There are many native species of ragweed, too, and it is a perennial weed. Others have a lot of issues with Bermuda grass, desert brooms, mesquite, different types of palm trees, junipers, Russian thistles, etc.