Bordello is a much nicer word, but we’ll stick to whore house for clarity in the title, I guess. I use brothel almost exclusively in my stories, but there are probably some innocent young readers who expect a brothel to be a soup restaurant or something completely different. You might be able to get some oyster crackers in a brothel, but don’t count on it.
Prostitution, or the now preferred sex work, is called the oldest profession for a reason. Think about it: as you, an ancient person, are out in the wilderness with no decent clothing and no pockets to store trade items like beads or apple pies. What do you do when you come across someone who is selling clothes with pockets? You really want the swag–nay, need the swag–but have only your swagger to trade. If you can’t sing or tell a story, you may have to just bone them to get those pockets. I’m sorry, that’s life in the bad old prairie. I didn’t invent humanity; don’t blame me.
If you remove any kind of moralizing and monogamy from human history, you essentially are left with lots of sex. Like the old song, birds to it, bees do it, octopuses do it even more often. We are only here because a huge number of humans had sex and many if not most of us are here because of some tax of sex work.
There are scholars of the history of sex work, and I am not one of them, yet. Still, I encourage you to read more about it and find out how many of your notions are cattywampus to the truth. Americans in particular have a twisted Puritan tradition of denying the importance (or existence!) of sex work. It surrounds us, like it always has, and you can’t wish it away without the kind of terrible unintended consequences that come with pretending things that aren’t real.

The District of Columbia was created in 1790, and yes, there was sex work aplenty all around, just like there were tons of incomprehensible hats to hide itchy wigs.
By the Victorian period, not only were there “red-light” districts in American cities, prostitution wasn’t illegal in most states here until the early 20th century.
Does criminalizing sex work hurt people? Probably. Like other measures, criminalizing it means that poorer people are made more vulnerable when their activity is outside the law. Meanwhile, people with means are able to get those clothes with pockets without much fear of consequences.
I’d say we all would be better off with more pandering and less slandering.
Further reading:
Colonial sex work via Slate: Were There Sex Shops in the Time of George Washington?
Late 19th century D.C. sex work via Boundary Stones blog: The Oldest Profession in Washington
The history of prostitution via Britanica: Prostitution
Further, further reading:
Undertakers, Harlots and Other Odd Bodies is out now. A free preview is available and all electronic formats are priced at a very reasonable US$3.99!!(Still $1.99 this week!!)
The paperback available through IndieBound is gorgeous, three dimensional, and handily delivered to your local independent bookstore for US$14.99.
Other places the print version is for sale (US$14.99, new) for the benefit of people who prefer paper: Amazon.com | Amazon.co.uk | IndieBound | BetterWorldBooks | Alibris
Ebook retailers: Apple | Kobo | Amazon.com | Barnes & Noble | Smashwords | Scribd