It depends on the desert. Three of our four deserts in North America are blanketed with cacti and other flora that can impale the careless. When hiking in the Sonoran, Mojave, or Chihuahuan Deserts, I only wear lightweight leather boots. These allow me to avoid the spines of cacti, agave, and other succulents that can pierce. Sandals are out, except for walking around base camp at the end of the day or when on a river trip.
The desert can be an unforgiving landscape if you are unprepared with the proper footwear. I recall reading how Geronimo and his Apache warriors would have to mend their buckskin moccasin soles every three days or 100 miles of travel!
For the past seven years, I have worn the S.W.A.T. Original brand boots ($90; originalswat.com) on all of my desert treks, and they have proven extremely reliable and affordable. Because I punish my footwear considerably, I tend to go through a pair about every eight months, so replacing a $300 pair of boots each season is not of interest. I have also had good luck with the Hi-Tec brand (hi-tec.com).
If I will be hiking in the Great Basin Desert amidst sagebrush, then I would consider wearing lightweight hiking shoes. I currently have a pair of Merrells (merrell.com) that have held up well.