I think what the muslim really claim is that when polygamy is legal then prostitution will go away. That is very obvious because things that people do that used to be called prostitution is now called marriage.
However, that’s misleading. The issue is government still interfere in all kind of marriage whether polygamy and monogamy and that would still make most people worst off. It’s not the poly that’s the issue. It’s the “gamy” and government’s “blessing”, “interferences”, and “regulations” that comes with marriage that prevents people from maximizing their selfish interests.
The short answer is yes. To add more details: