People used to move to dry climates for their health but these days I think just as many people in dry climates have allergies. In parts of Arizona, no one has lawns so if you're allergic to grass, it might help but when I've visited there I haven't noticed any difference in my allergy symptoms. Probably in the US people travel so much that everything gets spread around; no matter where you go, the same allergens are everywhere in the country. It probably wasn't the humidity but the fact that it is so far away and doesn't have a lot of cross contamination with US plants.
ETA: Humidity makes my hair frizz so I wouldn't like to live in a humid area. When you aren't used to it, it is difficult to adjust to it.