A good question is, "Why would Bill settle if he didn't do anything?" - but this is matched with "Wouldn't the accuser want Bill behind bars if he actually raped her?"
Money talks. It depends how much the accuser could be bought for. I suspect that almost all people could be bought if the price was right.
It basically depends on the financial situation of the accuser vs. how much is offered.
For the rare few that could not be bought, I doubt that they would place themselves in that type of situation to begin with.
It's not rare at all. Lots of cases (sex crimes and otherwise) go to trial and result in convictions, sometimes even confessions, after the victim declines a settlement.
Valid point if settling is cheaper and less time consuming than the court process. However, if you know your are innocent and choose the legal option instead of being extorted, and then if you are found not guilty after the court process, who then is responsible for the legal costs? I would hope that the accuser who made the allegations that were dismissed would be responsible for ALL legal costs on both sides (not that they would have that kind of money in many instances).
a fully legal option, it's not extortion.
As for this question of who is responsible for the legal costs, it depends on what the court awards. It's not a given that the false accuser would be responsible for all legal costs on both sides.
This is especially clear in cases where the government sues a private entity and the private entity is not found guilty. The private entity still ends up paying for their own legal fees. The government doesn't pay.
In my state, for example, our Attorney General seems to enjoy suing hospitals with flaky, half-baked reasons and in every case the hospital has been found not guilty - but they still have to foot the bill for all their legal fees. And of course, we taxpayers get to pay for the AG's frivolity.