While I think that it's stretching things to say that prostitution is something that no woman would engage in willingly in Eorzea, it does seem to be the case that it's considered a profession that is "beneath" a proper young lady. The prostitutes you actually talk to in the game seem, generally, to be fine with their line of work; they do not seem to be ashamed of what they do for a living, or wish they were doing something else. On the other hand, many quests allude to women who have barely escaped prostitution, painting it as some kind of dire fate worse than death.

The same kind of split in attitudes exists in real life. I've interacted with woman who've actually reminisced fondly of their days as prostitutes, who considered it to have been a positive experience. At the same time, it's considered to be a "dirty" profession, to the point that it's actually illegal; no parent wants their daughter (or son, for that matter) to become a prostitute. Unfortunately, making it illegal doesn't stop it from happening, but it does encourage human trafficking to keep the brothels full, and it does discourage prostitutes from seeking legal protection when they encounter dangerous or unpleasant clients.