If you have money, you could go on vacation to a country where it is legal. I believe it doesn't cost a lot, obviously make sure you're safe.
I don't know why it's illegal. There are women who marry men to just get out of their countries. Instead of marrying, they might prefer to trade in sex for a while, and build up money and move on to other things. They are right now selling themselves to one man, there is no one around to protect them, if they complain they will probably end up being back in their country. A brothel could provide protection. I don't think having relations with many men is better for a woman than one man, but there's more financial and physical security working at some place.
I don't think I'd want to go and be with a woman who's had more partners that day than I had ever ... so I don't think everyone automatically would run to brothels.