I don't know why it's illegal, but I can give you 3 good reasons why it should be:
(1) The USA can tax the sale of sexual acts (Think red light district or the Bunny ranch in Nevada)
(2) It would allow for the Department of Health to enforce strict STD testing by the brothel houses that hire these women, that way reducing the spread of HIV and HEP C, as well as other STD's.
(3) It would allow for prostitutes to not fear getting physically abused (beaten/mugged) while on the job. There are many prostitutes whose clients physically beat them after sex and take all of their money, only to have nowhere to go and file a complaint or get help since it is an illegal act. If you legalize it, prostitutes will have a venue where they can offer their services and also receive the protection of onsite security personnel.
"1"