Investing in sex tourism allows you to regulate and monitor it. It makes something that will inevitably happen anyways profitable and safer. There are perfect models of this all over Europe. It is better for government, for the woman, and for the clients. This system would solve the problems involved in prostitution.
I understand that there are many poor countries in the world. However, that doesn't mean that the "sex industry" should be one of the major livelihoods of the people who live in those countries. It is immoral to sell sex as a way of living. A better thing that a developing country could do is to invest in education, infrastructure, etc. (things that all nations should have in order to insure that their citizens have a relatively good standard of living) instead of investing in a morally corrupt practice in which adults can have an excuse to engage in what may otherwise be called pedophilia (I'm referring to child prostitution).
It would be immoral for governments to take an active role in the sex trade. This underbelly of society will always exist, but to promote it openly, profit from it, and advertise the exploitation of young women and men (sometimes underage) is wrong. Governments are not businesses, and should not promote amoral behavior to make money. Perhaps governments can regulate and protect this industry, but not promote it.
Sex tourism in a developing country is a recipe for disaster. Often times, if it exists in a place where people are hard to find work, young girls end up becoming prostitutes to support their family. This promotes sex trafficking and will degrade the overall morality of the nation and make tourists regard it as a low class destination.
The sex trade is demeaning to women. Developing countries shouldn't market sex as a way to make money. Locals would get in on the action, starting with young girls who become prostitutes. Crime would increase in the area. Drinking and other immoral things get worse as money flows into the area due to the sex industry. There would be too much demand for demeaning the self esteem of girls in the area.