I really hope you will air a dissenting view on rather than some inane moralizing or ideology. I don't often see this issue discussed in a way that reflects the reality I observed in a few locations in the EU. As someone who has worked as a volunteer with prostitutes in a loose medical capacity (alongside a wife working in a fully professional medical capacity), both in countries where it is legal, as well as in some with illegal brothels, I think that a rational appraisal of the evidence would make you rethink your unequivocal statement that you see "absolutely no reason it should not be legal." 

First, let me say that I lean relatively libertarian regarding social issues, favor legalization of pot and other drugs on the less destructive end of the spectrum, and in pure theory can see the case for prostitution as a valid economic activity when good faith consent exists.  However, reality does not bear out the claim that it has been made (or maybe even can be made) much less of a hellish situation for the women involved

In short: In countries with both legalized and illegal prostitution, even in Europe, most of the women/girls are trafficked to begin with.  Period.