It's also the world's oldest profession so there's obviously a lot of demand.
that's a lie, its not the worlds oldest profession. It didn't even come about till a currency was established.
You don't need currency for prostitution to take place. During The Russian Revolution, women used to prostitute themselves for half a loaf of bread.
I have no trouble believing that a caveman would offer a hungry cavewoman some meat after a successful hunting trip in exchange for no strings attached sex.
Even then its not the worlds oldest profession. Bread doesn't makes itself now does it
Bread is just one example, a more recent example.
Anything can be used as to barter for sex.
Perhaps a spot next to the fire, or some shiny object. non-marital sex has been very common in human society and there's no reason to doubt it hasn't always been that way, unless you contend earlier humans were somehow more moral than we are, which I highly doubt.