I said RAINN provided the spurious figure of assuming rapes happened at three times the reported figure. Not about the charge rate.
I have had some legal training so I'd like to try to explain. Quite simply police have to ask you these questions. The police do want to prosecute because it's their job and they get promoted for it, but they have to provide evidence strong enough for a conviction. If you don't have a DNA sample, if you don't want to tell them about how you got raped so they can procure eyewitnesses, if you don't want to give them your message history with the accused to show sexual intent, they simply can't do anything. Now there has been been a spread of the extremely damaging notion that women should keep these to themselves by painting it as patriarchal harassment. But these questions they would ask of stalking or theft or any other crime. And when you suggest to witnesses they shouldn't provide this evidence (which only they can give), you're making it harder to convict rapists.
A huge amount of extremely misleading studies have been produced to support the notion that there is a lax attitude towards rape, based on public figures and peppered with the occasional anecdote. And because of the basic problem with trying to show something didn't happen, instead of evidence these studies have been pushed by outrage. The forefront of that is the rapes charged number. It is a statistically irrelevant number, the actual relevant number would be to how many rape cases had reasonably strong evidence gathered but did not lead to charges. No actual attempt has been made to get these figures.
The basic drive to get people outraged is deeply unhelpful. It has turned a policy problem and a forensic problem into a political problem. Yes, it is not her fault she got raped. But the notion that just because she is the victim she shouldn't do anything is ridiculous. And yes, she does have a responsibility to report it. Any citizen has a responsibility to report a crime.