If you believe (which I don't because I've known a lot of prostituted women and men) it about starvation level survival sex work.. and you choose to stick your dick in them, do you think that makes you a rapist, or not? Because if I thought someone was only having sex with me to avoid starvation (for them or their children) I wouldn't. Because I'd consider that sexual assault.
So all the talk of 'choice' is a bit silly. The men using these women are rapists.
I strongly disagree and actually find your use of the term very offensive to real rape victims. When a sw (usually a woman) puts their services out there and someone pays for it, you might find it immoral and reprehensible, but is is not rape.
Rape is sexual penetration by force, against someone's will. When that person has consented, even if they only consented because they got paid, it is most certainly not rape.
In fact, if we were to take your argument to its logical conclusion, any time anyone has any kind of ulterior motive for having sex, the other person is a rapist. For after all, the consent was contingent on getting some kind of benefit.
Furthermore, any work of any kind would have to be considered slavery. Especially low paid work. Because the only reason the person is working at the min wage job - or most jobs for that matter - is their need to put food on the table.
Clearly the oft repeated fallacy that consent can't be bought is just that, and absurd fallacy. Consent can absolutely be bought, and to conflate a distasteful transaction with non-consensual sex both cheapens and dilutes the term rape, and is very offensive to real rape victims.
Putting that aside, the bigger problem with your stance is that you are only pretending to care for the sws, when in reality it's just enforcing your distaste for sexual transactions on others.
Think about it, these women (or a men for that matter) are desperate for money, and the only way they can get it is by selling sexual services. Well what happens if you're successful in dissuading every potential customer from buying those services?
The sws starve, that's what happens. They might have been in desperate straits to have decided to sell sex in the first place. But once they've embarked on this course, they are only harmed by do gooders interfering and going after their customers.