Follow up question, and apologies if this is better suited for AskScience, but is there solid science behind this? Cursory searches are turning up evidence of this being a common practice (e.g. the prevalence of sanatoriums in western states or former ASG John W. Trask advocating more time outdoors to combat TB), but having trouble finding any medical journals that validate it as it relates to arid climates. Closest I could find is this study posted on NIH that seems to corroborate Trask's assertions on fresh air, but doesn't address other climate factors.

I can contribute a piece to this answer: people certainly believed that the West could alleviate or prevent illness and this belief persisted well into the early twentieth century. Many people believed that disease was tied to climate. Promotional brochures targeting prospective homesteaders in the 1900s and 1910s often contained a section on the climate of the section, which would highlight how "healthful" and "invigorating" it was. They believed that the aridity of the West along with the dry air would help prevent the spread of disease. I can't answer to how many people believed this but one place you might look is Barbara Allen Bogart's Homesteading the Hight Desert. She uses oral history as her main source and one of the homesteaders might mention the climate health thing but I can't recall.