A number of places do exactly that, even providing fake prostitutes to lure the errant to their doom. Then they not only arrest them, but some newspapers publish the names of the arrested "johns" in order to dissuade others from the temptation. I do so love the righteous do-gooders of the world. Okay, that might be a bit tongue-in-cheek.
So what is wrong with that, given that prostitution is illegal? Do you think only the prostitutes are guilty?