Prostitution is a violent business, and if a community wants it out, they should have the right to make it illegal.
All of the reasons that you cite for prostitution to be illegal; health, drug possession, assault, murder, etc. are due to it being an unregulated illegal business. In Nevada, in the areas here prostitution is legal, the brothels have none of those problems.
So all you are left with is morality.
The real problem is that society while attempting (and failing) to regulate morality has created a breeding ground for disease, drug possession, assault, murder, etc.
Legalized and regulated prostitution will lead to a reduction in associated crime levels while police costs (and taxes) drop. Remember legalized prostitution means prostitutes paying taxes.
As for health reasons, don't buy that. So many of the American people are very active sexually and with multiple, very multiple, partners. Health reasons really couldn't not be the real reason doesn't really make a difference these days. Of course, STD has always been with us and certainly spread through prostitution, but that kind was usually curable, I have heard. Prostitution was illegal long before the horrific diseases we have today.
Prostitution has been illegal for may years before this massive drug problem, so that is not the reason. As for the assault, violence, if it were not illegal a lot of that would not happen.
Do not get me wrong, I do not advocate prostitution, I think it is an abomination, but it is a little hypocritical in this day and age to make it illegal.
There is another hypocritical side to prostitution - why are the customers not charged and prosecuted?
I don't think it is any of the above although many of the things you list are certainly a part of the prostitution scene - not speaking from personal experience - mind you.