Imagine how quickly the MeToo movement would fail if some of these well publicized accusations were publicly proven false. Thing is, it's very hard to prove a negative.
It's also hard to prove something is false when it is actually true. Generally, these things aren't coming to light unless there is a pattern, where more than one woman has been a victim. It becomes harder and harder to believe that the guy isn't some sort of abuser when people are independently stepping up. Most of these public firings have multiple accusations, even if the identity of the accusers isn't made public.
Do you really think that is a bad thing?
My problem with the incidents surrounding Cosby is that there are so many, I'm having a hard time believing that some of them aren't just hanger-ons, which is to say, some are true, and some are false. That doesn't mean that some of these women haven't been hurt very badly, but the idea that we should just believe every subsequent accusation is pretty dangerous.
As has been said in other answers, false accusers (whose identity is known) will be tarred and feathered by the community. Though not ideal (I think they should serve jail time), it is better than nothing.