> As to your second point, we often hire underage people to do work such as restocking shelves. If sex work is truly the same as retail work would you also argue that hiring an underage prostitute is no different than when Walmart hires a 15 year old to push carts? If not, what's the difference?

I don't find this argument compelling. Are you saying that the only professions that are morally permissible are those that we would allow fifteen-year-olds to do? We don't allow them to bartend, drive trucks, nor be members of the US Senate, but I find it silly to think that fact makes those professions particularly immoral. 15 year olds aren't even allowed to work 40 hour weeks in most countries.

And, to answer your question, I think the answer is that the fifteen-year-old is not sexually nor emotionally mature enough to engage in prostitution. (Just like they are not mature enough to serve alcohol or drive, whereas they are likely emotionally mature enough to push carts.) They're below the legal age of consent by three years, for goodness' sake! Advocating for legalized and regulated prostitution is not equivalent to advocating for pedophilia, and I find the equivalence you've drawn troubling.