No, it has no impact what so ever on the number of men who use prostitutes. There's the same problem with drug laws. When both the buyer and seller are willing, they'll do what it takes to circumvent the law. In Iran they have the death penalty for prostitution, but it's just as prevalent there as anywhere else.
All numbers I have access to are in Swedish.
http://www.bra.se/
All there research is available free on pdf and easy to download. The kink is that you need to know Swedish
Just to be clear on this. This is a govornement agency, they're not allowed to have opinions, only publish numbers. The official Swedish govornement line is the same as yours. But it's not based on science.
I think you're being extremly judgemental without any arguments other than just opinons to back it up.