People also deliberately make false claims about other crimes. Burglary so they can make dishonest insurance claim, GBH when they intend to get revenge on whoever it is who's been falsely accused.
A family connection was plagued by a woman who, as well as committing acts of vandalism against his relatives, made a series of allegations of assault against him.
Initially the police assumed my connection (a relative of a relative) had committed some low level offences but the woman quickly escalated, thank goodness. Her insanity became unmistakable.
Her final act was to call 999 claiming that my connection had broken in, tied her up and raped her. When the police arrived the ropes lay around her, as she said she had only just freed herself.
However the police smelled a rat and did some forensic work. They proved there had been no one else present and that the scene had been staged. On top of that, it turned out my connection couldn't have possibly done it. She was prosecuted and he has heard nothing further.
That's a case where the complainant should be prosecuted, but rape was only one of the charges she tried to have brought against a totally innocent man.
The percentage of deliberately false claims made of serious crimes is low, and AFAIK it's the same whether it's rape or the theft of valuable jewelry. In such cases prosecution may be suitable. However I am not sure that it's suitable for rape cases unless real malevolence can be demonstrated.
I think back to Jimmy Saville. How many of his victims might have been judged as wicked girls trying to smear a national treasure had they tried to get him charged?