I believe that the most widely used official reason is to prevent the spread STD's. But the real basis behind it is indeed the fundamentalist Protestant culture that now dominates the country, the whole "sex is a holy sacrament between only husband and wife" idea and not an act of enjoyable pleasure since that tempts men from the Holy Path, along with the great double standard that unmarried women who have sex are considered dirty and immoral and unholy, while men who do so are not (witness the perjorative terms "slut" and "whore"), and so women who sell sex are seen as Evil Incarnate. I know here in Wisconsin there was a time not that long ago is which it was actually illegal to have sex with someone you weren't married to; the current law against prostitution still states as such.
During the days of the Old West, when many places were founded as cattle towns, railroad towns, mining camps and other male-dominated settlements, prostitution was widespread, with saloons acting as brothels. Then when they became "civilized" with the mass arrival of thr wives and families from back east and the clergy, prostitution soon was pushed out and then outlawed. The reason it still exists in Nevada, in certain counties defined by law, is that Nevada has always had a libertarian culture, it being founded alomost solely by miners and railroad workers. A "live and let live" philosophy was adopted to prostitution. The brothels in several of the towns along I-80 for (Elko for example) are still inside the town or even in the downtown area, and not pushed outside the city limits like in other places.
Imagine how different this country could have been had Spain taken a far stronger interest in the part of North America above their Mexico territory, and kept the British away. There could have been a Hotel Del Rey or Zona Blue everywhere here now, and Miami could have been like Rio but ten times better (yes I know Brazil was Portuguese, same difference).
