People are way too hung up on morality. It is not moral for people to have sex? Is it not moral for people to make money? Is it not moral to make money having sex?
Listen, sex is fun. The people who work in the industry that I know (yes mostly 1st world countries) love what they do. To us sex is totally a natural part of who we are and enjoy having sex and being involved with people with that level of connection.
Prostitution is legal in almost all countries - it is not a big shocker! But for some reason the US thinks that sex is some taboo thing, even with their own partners. We have a "don't talk about it" attitude about sex.
It is healthy and normal. Now, I do believe there needs to be regulations and that it can not be something people are forced into or hurt by. Brothel owners, Madams and the like are fine, but only if they are regulated and the women and men who work in the industry are treated with respect and kindness and allowed the freedom to come and go as they wish and only perform sexual acts with who they wish.
The problem isn't the idea of the sex industry or the sex workers, the problem is with the corruption that goes along with not having a system in place to protect sex workers.
I don't know if sex will rejuvenate an economy - the problems countries have are much larger than sex can fix. But, allowing for a safe environment for people to have sex and make money should not be a crime.
If you're willing to look past the morality and image concerns, sex does not fail. There's always a demand for it, a demand only limited by how much of it can be provided. As a long term solution you're going to need more than thriving pornography to put your country on top, but if truly desperate, it'll move some money.
If an economy is based and run on sex, what is the outcome of that? You have to think about the conditions of the sex industry. They may give a temporary boost in the economy, but in the long-term, they produce more children that cannot be clothed and fed, more women who cannot support their children and themselves, more uneducated children because the women cannot get them to school, and in the end, MORE DEFICIT.
It is pretty sad when a country resorts to sex and the sex industry when in times of need. If they wanted to do this then more power to them, but it will fail. The sex industry is hurting in thriving counties, so there is no reason to believe that it will do well in one that has a struggling economy.