False positives are never a _should_ thing, they're a "best we can do, and worth the cost" thing (or not). It's entirely reasonable to push for a better system, one with fewer false positives (and false negatives).
I think preventing other crimes is similar. There will always be injustice on some side of the issue. And I’m not trying to argue that that means the status quo is great! But I don’t think we will eventually hone in a perfect system. Maybe just circle around some imaginary point, refining rules and processes until the whole thing breaks down.