Hi there! i think it would be a fabulous idea! I know I hired one when I had children with me during a visit. Babysitting is pretty big business in Las Vegas, one would think. I know I simply pulled out the Yellow Pages and found a nice grandma type and ordered her delivered to my hotel room. May seem sort of impersonal, but in Vegas they are all licensed & certified, plus checked out thoroughly, an F.B.I. background check I'm told. My babysitter belonged to a particular Agency, and carried a badge with all her information, accreditation & identification.
My children were simply sleeping the entire time I was gone, from late evening to wee hours of the morning, but Las Vegas NEVER sleeps, so an around the clock business sounds idea! Just have to iron out all the details, but I think you have something there!

Good Luck, Tina C.