When you make the sale of something illegal, you raise its price. This should be clear in the case of sex and prostitution where the effort that men go through to get sex where prostitution is illegal is worth considerably more than the price of a prostitute where it is legal. By lowering the price of sex, prostitution elevates the value marriage in relative terms. Legal prostitution eliminates the unfair advantage of women's sexual power because it makes sex available at a fair price.
Today prostitution is illegal in America. In fact the decay of America exactly parallels the attack on prostitution. I don't know the situation in Europe. But in all moral cultures in history that I know of, prostitution was tolerated. I believe that eliminating prostitution is guaranteed to destroy morality because this causes men to chase all women and thereby destroys the chastity of women.
> It's no coincidence that in all of humanities history most scientists and other pioneers were little interested in sex or even asexual in many cases.
I know of a few cases of this, but what evidence do you have that this applies to MOST?
> I do believe that men's sexual drive can be hold under control because many societies (nowadays primarily Islamic ones) manage to accomplish this.
The societies that try this seem to be a mess. I think you would have to live in one of these societies for a while to really understand what is happening there.
> What's your personal history? Were you ever in need of prostitutes? I doubt it.
For several years before I could look abroad for a wife, I used prostitutes weekly and this kept me sane.
> Me neither, just like all of my muslim friends and their families.
How old are you? A man who is young and expects to marry soon can probably control himself.
> Also a concubinage system would be an incredibly superior system to a prostitution system.
Concubinage is horrible and should be illegal as it is in the Old Testament. With prostitution, a small number of prostitutes can service the entire male population, allowing the other women remain chaste. Concubines don't do this and are just an inferior form of marriage which is unfair to women.
I urge you to study history which is the primary source of knowledge. On prostitution, you can read this:
https://www.amazon.com/Love-Sale-World-History-Prostitution-ebook/dp/B006NZAQH8/