The problem of "n" does not completely go away even in a much improved legal system. Assuming you can identify the killer 99.99% correctly with absolute certain

The problem of "n" does not completely go away even in a much improved legal system. Assuming you can identify the killer 99.99% correctly with absolute certainty, you will still have that one in ten thousand case where the killer is not precisely known, but there is 50%, 90%, 99% probability it's them, that is, you risk to convict one innocent man for every n = 1, 10, 100 guilty persons in those rare cases. So the efficiency of the criminal system and the problem of "n" are somewhat orthogonal: the first is an issue of effective governance, the second is a political choice faced by any practical (thus, imperfect) system of governance.