The Economist offers us an especially ill-defended version -- the author doesn't really find the liberal view of man needs any defense at all, and so simply assumes it as incontrovertible. This serves to make the assumptions stand out. The title itself implies that there exist a sharp line, assumed throughout liberalisms, that there are two sharply distinct spheres: the personal choices, over which no one at all has any say other than the chooser, and public choices, which can be regulated. But has been pointed out before, this line is arbitrary, and can be drawn pretty much wherever the drawer wishes, since all choices have both personal and public aspects. What happens in practice is that for some question where a liberal theorist wants the activity to be legal, he highlights the private aspects, but if he wants it to be illegal, he highlights the public aspects. (Buying a gun is, of course, "a personal choice," but I will lay odds that this writer, looking at that choice, will focus on "the epidemic of gun violence" instead of the personal choice!)
"NIMBYs make common cause with puritans, who think that women selling sex are sinners, and do-gooders, who think they are victims. The reality is more nuanced. Some prostitutes do indeed suffer from trafficking, exploitation or violence; their abusers ought to end up in jail for their crimes. But for many, both male and female, sex work is just that: work."
Notice that only a "puritan" could think that taking money so that others can use your body as a sperm repository is a sin! Furthermore, once it is determined that something is "work," it has to be allowed. The fact that contract killing is also "work" doesn't seem to have occurred to the author.
In the Classical-Christian conception of law, the right question to ask when considering legalizing prostitution is not, "Is it a choice?" (since murder, after all, is a choice!) or "Does it violate anyone's rights?", but "Is the common good better served by forbidding or by allowing this activity?"
Thus we find in the Middle Ages a sensible, moderate policy towards prostitution: often it was legal, but only within defined areas (the red light district). A figure as august as Augustine argued that forbidding prostitution "would bring lust into all aspects of the world."
But as with drugs, we have lost all common sense, and can only oscillate between the extremes: if something is wrong, the wrongdoer must suffer prison, and if it is not worthy of legal penalties, then it must be permitted everywhere: it is just a "choice."