Every study not sponsored by a religious unit / right moral high ground type has shown your conclusions to be false. The fact that it is illegal is what leads to more trafficking... is what leads to more public health issues.. pushes people underground which brings in the deplorable element... and makes it more dangerous for them.
Making prostitution legal between consenting adults, where it can be practiced in areas that are not in the public eye and can be licensed and regulated, removes many deplorables from the equation and also reduces many trafficking, public health, and safety issues. Is it the ideal way to act? Maybe not for everybody, but it will happen, so why willingly make society more dangerous.
All that being said, that is the law and it is illegal. This also involved those who are younger and are easily influenced. While I think prostitution in a controlled environment between consenting adults is fine, I have more issues when it takes place with teenage kids on a recruiting mission. I do think the penalty should be quite severe.