Hear me out, if you don't go public with a false rape accusation, but only report it to the police, and it gets proven false, you mostly waste time for the law enforcers, and the accused, while having gone through some hardship, at least can recover his life back to normal quick enough.

If you go public with it, you also waste time of maybe millions of people who learn about the accusation and waste time either white knighting or trying to figure out if the claim is likely true or false. On top of that, even assuming the false claim gets proven 100% false (which is unlikely, since it can be insanely difficult to prove something didn't happen, and it's an unreasonable legal standard to hold to), very few people of those that heard about the initial claim will also hear about the accused's innocence, and even fewer will actually believe it, leaving the accused forever a pariah, unable to resume his normal life. Thus, much more damage is being caused to not only the accused but to society itself once you make your false rape claim public, and you should be punished accordingly for it.