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.Maybe it's not the humidity, but it's as whateve said, and if I had stayed longer, I would have developed allergies to something local. I wonder if people in low humidity places have fewer allergies? One of my coworkers said the same about Costa Rica, that her allergies went away. She thought it was because of greater biodiversity in the flora, that if you were allergic to something, there wasn't the sheer number of the same tree/flower of it like we have here. I'm trying to think back to when I lived abroad. The longest I lived abroad was 1 year, but I also did a stint for 5 months, 8 months, another for almost 3 months. I can't remember my allergies being that bad in those places, but it was a while ago ...
anyway, even if the effect of humidity on allergies is unclear, definitely it is better for your skin and hair.
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.