Child Services: Going too far?

[Isolde]

"Tiz better to let 20 guilty men go free than convict 1 innocent."

That's a pretty common catchphrase, but is it really as simple as that? It might make sense if those twenty guilty men you let free are unlikely to repeat their crimes, but that's unlikely.

What if you had 21 suspected serial killers, of which you know that at most one is innocent? If you allow all of them free, each of the killers is likely to kill again, possibly multiple times. You don't have the resources to watch all of them after you let them out, and it's close to certain that at least some of them would elude surveillance anyway.

With imperfect information, it isn't possible to never falsely convict someone. This is why we have "beyond a shadow of a doubt" and "innocent until proven guilty", but both whitewash a rather distressing margin of error. Therefore, taken to an extreme, your statement would require that we never punish anybody?

I empathize with the principle of it, but what I'd like to know is WHY you think this.