But all those have recourse. They can sue the state and get restitution. So, yes, mistakes happen, but there is procedure to seek corrective action. There is a difference.
The only way to not investigate innocent people would be to know in advance who's guilty. And if you knew who was guilty in advance why even have courts? It'd be for show. Anyhow, that's be asking for more than we are capable of as a civilization. It's understood innocent people will be accused and acquitted thru the system; if the state is proven wrong and you suffered from the process, there is recourse. You sue the state.
How do you sue vigilantes who are by definition, outside the system?
No, I mean like everybody who ever got slandered by anyone in everyday life with no consideration, due process or authority at all. Because that's how this vigilante thing works.
It's not just being accused (or considered suspect) of something that's problematic, it's HOW and by WHOM this happens.
A police investigation can look into the wrong person too, sometimes can even convict (and even execute!) the wrong person, but there are tons of checks and balances in action there. And "the people" have chosen to have the police and judicial system do that work, not Anonymous.
You mean like Richard Jewell, Bruce Ivins, and David Kelley?