I remember seeing evidence that people deliberately make up rapes about as often as they make false reports of other serious crimes, like burglary and assault. It's rare, only about 3% of reports
We prosecute people who lie about burglary to make a false insurance claim, and we should prosecute malicious claims of rape too, as long as they definitely are malicious, and particularly those that result in someone going through a police investigation with all the stress that involves. As PP have said, the name of a suspect often slips out and they may be tainted forever.
This is a completely separate issue to the dismal conviction rate for rape. We should, as a society, be looking at how to improve the criminal justice system.