This isn't so much a historical question as just a question about how societies work, so here's a partial answer. One short answer is that as people have fewer and fewer rights, as women have fewer and fewer rights, they start to be seen as property, and in any society where people are seen as property, you don't just go and use somebody's property without talking to the owner, i.e. pimp/husband/father.
What I'm saying is that the fewer "rights" someone has, the more rights those over him/her have, and in general, people are jealous of their power, and would fight against anyone taking what they want free of charge.
The second question relevant is what exactly is the item of transfer in prostitution. While yes, sex is often pretty central, there's always more, be it power, be it companionship, conversation, domestic help - an emotional connection. Whether it's Geishas, comfort girls, temporary marriages, or country wives, an awful lot of what many cultures have determined men "want" when it comes to their local variants of prostitution and not things that can simply be taken.
Looking back over what I've just argued, I suspect that the danger to women comes not when women have very few rights, because likely any lack of rights on the part of women is going to be somewhat balanced out by the rights of those who see them as property. The real danger, the places in history where a male could simply "take what they want" is when people have no rights - especially where specific social groups have no rights, where certain families and communities have no rights in the face of other communities which are in a position to exploit, coerce, or simply take.
Most women were either someone's wife or someone's Daughter. Even if they had no protections, the men were legally protected from their women being "defiled". Hammurabi even had laws about this.
If a man wish to separate from a woman who has borne him children, or from his wife who has borne him children: then he shall give that wife her dowry, and a part of the usufruct of field, garden, and property, so that she can rear her children. When she has brought up her children, a portion of all that is given to the children, equal as that of one son, shall be given to her. She may then marry the man of her heart.
This is one of the only segments I could find that specifically mention prostitutes.
If a "sister of a god," or a prostitute, receive a gift from her father, and a deed in which it has been explicitly stated that she may dispose of it as she pleases, and give her complete disposition thereof: if then her father die, then she may leave her property to whomsoever she pleases. Her brothers can raise no claim thereto.
So in essence Women could not be much treated worse than Men, they just had less than equal protection when it came to property issues. They were still Human beings
Your question is problematic.
First of all, which "rights" are we talking about? Civil, criminal? What about societies where civil and criminal were not meaningful categories?
Rape is almost universally illegal in all cultures, independent of the rights women have (to use our contemporary verbiage) since it is a crime/violation vs either the father of the girl or the husband.
The other concept that is problematic in your post is "prostitution". The idea that a woman exchanges sex for money in a transaction is somewhat new; certainly, the exchange was not regarded as legally binding in any sense until quite recently (in Germany, for example, since roughly the 1990s).
In ancient cultures the flow of resources from men to women may have had sex as the trigger, or in some ancient Middle Eastern cultures (take Babylonia) the prostitution would have been religiously ritualised.
I suppose I would ask, "were men actually paying for sex?"
Sadly, that question is outside of my wheelhouse.