I have been doing a lot of barefoot running but mostly on the roads and sidewalks. I have to be careful in some areas. The desert is not pristine! There are a lot of sand dunes here but there are also a lot of rocks and small rock outcrops / hills called jubals.
One type of hazard are these little burrs from the desert bushes. When you step on them they stay attached and love to settle between your toes. They won’t come off until you stop and pull the little buggers off. Vibrams are a pretty good choice in these areas.
People have been chucking junk into the desert since Lawrence. There are all sorts of rusty metal bits lurking just above and below the surface. Again Vibrams are the way to stay protected, but even then I was once jabbed by a cactus needle right through the rubber sole.