I've been in the desert for 20 years now. The nosebleeds for me happen when I travel to and from the Midwest every other summer. I too dislike humidity...ugh. My friend has been in Thorndale, TX for the last five months...he desperately wants to be back in Albuquerque...the humidity, while at 39-50% every day and the temps in the upper 90s...is unbearable to him. I don't really blame him. Kansas City last year was pretty yucky with upper 90s and 60% humidity (which led to some supercells later that day...)
Right now the humidity here in the Albuquerque area is about 5%, with temps in the upper 90s. The cooler is blowing 77*F air...pretty comfortable. Swamp coolers generally start to suck when it either rains (it gets really humid inside, but thanks to rain cooled air, it doesn't start to heat up the house at the same time) or we get a humid spell (generally in mid to late July, early to mid August, and occasionally in September here...). I do remember a few summers in El Paso when the Monsoon season was in full swing. It would be 95*F outside, and the humidity around 30%. My grandfather's house would be unbearable.
Generally, the new trend in desert homes is refrigerated air. "Green" homes (at least in Albuquerque) will generally have one or two swamp coolers instead of one big A/C system. I find in my neighborhood (a mix of late 70s, early 80s to mid 90s homes) have swamp coolers...however some of my neighbors have converted...the houses around here were not built for such.
Since my house had its garage converted into a room, we just crack the interior garage door when the swamp cooler is on...we have attic access in there, so we're cooling the attic...it might sound like we're wasting energy, but cooling the attic down means keeping the rest of the house cooler...and since the attic has vents, there's no need to crack a window.